# Technical reports from 1995

## Numerical Analysis Group Research Reports from 1995

The Numerical Analysis Group has a technical report series with hundreds of titles going back to 1984. Most of these articles have been published, or are submitted for publication, in journals or conference proceedings. This is a list of reports from 1995 to today.

Details and electronic copies of technical reports can be found in the Maths Eprints Archive (all links below point to this archive).

There is a separate list of Research Reports printed before 1995, most of them are not available electronically.

Numerical Analysis Group Research Reports are also printed as A5 booklets, and copies can be obtained by contacting the Numerical Analysis Group Administrator

**2015NA-15/14
**

*Multiple local minima of PDE-constrained optimisation problems via deflation*

P. E. Farrell

**NA-15/13**

*On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space*

D. P. Hewett and A. Moiola

**NA-15/12**

*Expander $\ell_0$-Decoding
*R. Mendoza Smith and J. Tanner

**NA-15/11
**

*Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method*

I. Smears

**NA-15/10**

* A fast and well-conditioned spectral method for singular integral equations*

R. M. Slevinsky and S. Olver

* Global convergence rate analysis of unconstrained optimization methods based on probabilistic models*

C. Cartis and K. Scheinberg

* Representation using the Weyl transform
* Q. Qiu, A. Thompson, R. Calderbank, and G. Sapiro

* On block coherence of frames*

R. Calderbank, A. Thompson, and Y. Xie

* Computing planar and spherical choreographies*

H. Montanelli, and N. Gushterov

* Computing eigenvalues of real symmetric matrices with rational filters in real arithmetic
*A. P. Austin, and L. N. Trefethen

* Fast algorithms for spectral differentiation matrices*

J Aurentz

*The Remez algorithm for trigonometric approximation of periodic functions** *M Javed and L N Trefethen

*Extension of Chebfun to periodic functions*

G Wright, M Javed, H Montanelli and L N Trefethen

*Mathematics of the Faraday Cage*

**2014**

*Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using H*

*ö*

*lder continuous gradients*

*The impact of startup costs and the grid operator on the power price equilibrium*

*An upper bound on the convergence rate of a second functional in optimal sequence alignment*

*A general duality relation with applications in quantitative risk management*

*The existence and uniqueness of a power price equilibrium*

*Calculation of a power price equilibrium*

*A simple proposal for parallel computation over time of an evolutionary process with implicit time stepping*

*Shadow boundary effects in hybrid numerical-asymptotic methods for high-frequency scattering*

*Deflation techniques for finding distinct solutions of nonlinear partial differential equations*

*Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens*

*A preconditioned MINRES method for nonsymmetric Toeplitz matrices*

*Low rank matrix completion by alternating steepest descent methods*

*Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples*

*CGIHT: Conjugate Gradient Iterative Hard Thresholding for Compressed Sensing and Matrix Completion*

*Active-set prediction for interior point methods using controlled perturbations*

*Fast sparse kernel summation on Cartesian grids*

*Convexity and solvability for compactly supported radial basis functions with different shapes*

*Extension of continuum time-dependent Hartree-Fock method to proton states*

*Conjugate Gradient Iterative Hard Thresholding: Observed Noise Stability for Compressed Sensing*

*An Algorithm for the Convolution of Legendre Series*

N Hale and A Townsend- NA-14/01
*Continuous analogues of matrix factorizations*

A Townsend and L N Trefethen

**2013**

- NA-13/26
*A frequency-independent boundary element method for scattering by two-dimensional screens and apertures*

D P Hewett, S Langdon and S N Chandler-Wilde- NA-13/25
*Acoustic scattering by fractal screens: mathematical formulations and wavenumber-explicit continuity and coercivity estimates*

S N Chandler-Wilde and D P Hewett- NA-13/24
*Well-balanced r-adaptive and moving mesh space-time discontinuous Galerkin method for the shallow water equations*

S Rhebergen- NA-13/23
*Efficient smoothers for all-at-once multigrid methods for Poisson and Stokes control problems*

S Takacs- NA-13/22
*Natural preconditioners for saddle point systems*

J Pestana and A J Wathen- NA-13/21
*The antitriangular factorisation of saddle point matrices*

J Pestana and A J Wathen- NA-13/20
*A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing*

C Cartis and A Thompson- NA-13/19
*Preconditioned iterative methods for Navier-Stokes control problems*

J W Pearson- NA-13/18
*On the role of commutator arguments in the development of parameter-robust preconditioners for Stokes control problems*

J W Pearson- NA-13/17
*A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions*

M Javed and L N Trefethen- NA-13/16
*A fast, simple, and stable Chebyshev-Legendre transform using an asymptotic formula*

N Hale and A Townsend- NA-13/15
*The exponentially convergent trapezoidal rule*

L N Trefethen and J A C Weideman- NA-13/14
*Numerical algorithms based on analytic function values at roots of unity*

A P Austin, P Kravanja and L N Trefethen- NA-13/13
*On non-overlapping domain decomposition preconditioners for discontinuous Galerkin finite element methods in H*^{2}-type norms

I Smears- NA-13/12
*Efficient high-order rational integration and deferred correction with equispaced data*

S Güttel and G Klein- NA-13/11
*A robust all-at-once multigrid method for the Stokes control problem*

S Takacs- NA-13/10
*A robust multigrid method for the time-dependent Stokes problem*

S Takacs- NA-13/09
*Fast Solvers for Cahn-Hilliard Inpainting*

J Bosch, D Kay, M Stoll and A J Wathen- NA-13/08
*Computing the common zeros of two bivariate functions via Bezout resultants*

Y Nakatsukasa, V Noferini and A Townsend- NA-13/07
*On the spectral distribution of kernel matrices related to radial basis functions*

A J Wathen and S Zhu- NA-13/06
*Relative Robust Portfolio Optimization*

R Hauser, V Krishnamurthy and R Tütüncü- NA-13/05
*Performance Comparisons of Greedy Algorithms in Compressed Sensing*

J D Blanchard and J Tanner- NA-13/04
*Automatic linearity detection*

A Birkisson and T Driscoll- NA-13/03
*Discontinuous Galerkin finite element approximation of Hamilton-Jacobi-Bellman equations with Cordès coefficients*

I Smears and E Süli- NA-13/02
*Gaussian elimination as an iterative algorithm*

A Townsend and L N Trefethen- NA-13/01
*An extension of Chebfun to two dimensions*

A Townsend and L N Trefethen

**2012**

- NA-12/19
*Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach*

A Townsend, V Noferini and Y Nakatsukasa- NA-12/18
*Application of Fredholm integral equations inverse theory to the radial basis function approximation problem*

R Renaut and S Zhu- NA-12/17
*Discontinuous Galerkin finite element approximation of non-divergence form elliptic equations with Cordès coefficients*

I Smears and E Süli- NA-12/16
*A Monte Carlo Approach to the Fluctuation Problem in Optimal Alignments of Random Strings*

S Amsalu, R Hauser and H Matzinger- NA-12/15
*Distribution of Aligned Letter Pairs in Optimal Alignments of Random Sequences*

R Hauser and H Matzinger- NA-12/14
*Fast iterative solution of reaction-diffusion control problems arising from chemical processes*

J W Pearson and M Stoll- NA-12/13
*Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights*

N Hale and A Townsend- NA-12/12
*Some observations on weighted GMRES*

S Güttel and J Pestana- NA-12/11
*Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems*

J W Pearson, M Stoll and A J Wathen- NA-12/10
*Compactly supported radial basis functions: How and why?*

S Zhu- NA-12/09
*Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology*

L Diening, C Kreuzer, and E Süli- NA-12/08
*Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection*

S Güttel- NA-12/07
*Convex hull property and maximum principles for finite element minimizers of general convex functionals*

L Diening, C Kreuzer, and S Schwarzacher- NA-12/06
*Chebfun and numerical quadrature*

N Hale and L N Trefethen- NA-12/05
*Preconditioners for state constrained optimal control problems with Moreau-Yosida penalty function*

J W Pearson, M Stoll and A J Wathen- NA-12/04
*Chebyshev interpolation for functions with endpoint singularities via exponential and double-exponential transforms*

M Richardson- NA-12/03
*A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions*

S Güttel and L Knizhnerman- NA-12/02
*A fast and well-conditioned spectral method*

S Olver and A Townsend- NA-12/01
*Convergence of linear barycentric rational interpolation for analytic functions*

S Güttel and G Klein

**2011**

- NA-11/20
*Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows*

S Congreve, P Houston, E Süli, and T P Wihler- NA-11/19
*Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian*

C Kreuzer- NA-11/18
*Parameter estimations for cerebrospinal fluid infusion test*

A Eisentraeger, I Sobey and M Czosnyka- NA-11/17
*Adaptive Galerkin approximation algorithms for partial differential equations in infinite dimensions*

C Schwab and E Süli- NA-11/16
*Finite element analysis of Cauchy-Born approximations to atomistic models*

C Makridakis and E Süli- NA-11/15
*Fast iterative solvers for convection-diffusion control problems*

J W Pearson and A J Wathen- NA-11/14
*Robust Padé approximation via SVD*

P Gonnet, S Güttel and L N Trefethen- NA-11/13
*Combination preconditioning of saddle point systems for positive definiteness*

J Pestana and A J Wathen- NA-11/12
*A Short Note on the Fast Evaluation of Dihedral Angle Potentials and their Derivatives*

P Gonnet- NA-11/11
*Stability of barycentric interpolation formulas*

M Webb, L N Trefethen and P Gonnet- NA-11/10
*Regularization-robust preconditioners for time-dependent PDE constrained optimization problems*

J W Pearson, M Stoll and A J Wathen- NA-11/09
*Numerical inverse scattering for the Korteweg–de Vries and modified Korteweg–de Vries equations*

T Trogdon, S Olver and B Deconinck- NA-11/08
*An efficient implementation of an implicit FEM scheme for fractional-in-space reaction-diffusion equations*

K Burrage, N Hale and D Kay- NA-11/07
*Six myths of polynomial interpolation and quadrature*

L N Trefethen- NA-11/06
*A radial basis function method for solving PDE constrained optimization problems*

J W Pearson- NA-11/05
*Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers*

J W Barrett and E Süli- NA-11/04
*Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators with unbounded drift*

L E Figueroa and E Süli- NA-11/03
*A sinc function analogue of chebfun*

M Richardson and L N Trefethen- NA-11/02
*Robust rational interpolation and least-squares*

P Gonnet, R Pachón and L N Trefethen- NA-11/01
*Ten digit problems*

L N Trefethen

**2010**

- NA-10/15
*Automatic Fréchet differentiation for the numerical solution of boundary-value problems*

A Birkisson and T A Driscoll- NA-10/14
*A New Approximation of the Schur Complement in Preconditioners for PDE Constrained Optimization*

J W Pearson and A J Wathen- NA-10/13
*All-at-once solution of time-dependent PDE-constrained optimization problems*

M Stoll and A J Wathen- NA-10/12
*A high-order approximation method for semilinear parabolic equations on spheres*

H Wendland- NA-10/11
*Multiscale RBF collocation for solving PDEs on spheres*

Q T Le Gia, I H Sloan and H Wendland- NA-10/10
*An extended error analysis for a meshfree discretization method of Darcy's problem*

D Schräder and H Wendland- NA-10/09
*Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems*

P Giesl and H Wendland- NA-10/08
*Computation of equilibrium measures*

S Olver- NA-10/07
*On choice of preconditioner for minimum residual methods for nonsymmetric matrices*

J Pestana and A J Wathen- NA-10/06
*Optimal Multilateral Well Placement*

C L Farmer, J M Fowkes and N I M Gould- NA-10/05
*A general framework for solving Riemann-Hilbert problems numerically*

S Olver- NA-10/04
*Preconditioning iterative methods for the optimal control of the Stokes equations*

T Rees and A J Wathen- NA-10/03
*A robust implementation of the Carathéodory-Fejér method*

J van Deun and L N Trefethen- NA-10/02
*Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev points*

R Pachón, P Gonnnet and J van Deun- NA-10/01
*A note on the solution of a poroelastic problem*

B Wirth, I Sobey and A Eisenträger

**2009**

- NA-09/09
*Numerical solution of Riemann-Hilbert problems: Painlevé II*

S Olver- NA-09/07
*Computing the Hilbert transform and its inverse*

S Olver- NA-09/06
*A second-derivative trust-region SQP method with a "trust-region-free" predictor step*

N I M Gould and D P Robinson- NA-09/05
*How fast do radial basis function interpolants of analytic functions converge?*

R B Platte- NA-09/04
*Impossibility of approximating analytic functions from equispaced samples*

R B Platte, L N Trefethen and A B J Kuijlaars- NA-09/03
*GMRES for oscillatory matrix-valued differential equations*

S Olver- NA-09/02
*Fast, numerically stable computation of oscillatory integrals with stationary points*

S Olver- NA-09/01
*On solving trust-region and other regularised subproblems in optimization*

H S Dollar, N I M Gould and D P Robinson

**2008**

- NA-08/21
*A second derivative SQP method: Local convergence*

N I M Gould, D P Robinson- NA-08/20
*Barycentric-Remez algorithms for best polynomial approximation in the chebfun system*

R Pachón and L N Trefethen- NA-08/19
*Preconditioned GMRES for oscillatory integrals*

S Olver- NA-08/18
*A second derivative SQP method: Theoretical issues*

N I M Gould, D P Robinson- NA-08/17
*Local projection finite element stabilization for the generalized Stokes problem*

K Nafa and A J Wathen- NA-08/16
*Conformal Maps to Multiply-Slit Domains and Applications*

N Hale and T W Tee- NA-08/15
*Using global interpolation to evaluate the Biot-Savart integral for deformable elliptical Gaussian vortex elements*

R B Platte, L F Rossi and T B Mitchell- NA-08/14
*Chebyshev semi-iteration in Preconditioning*

A J Wathen and T Rees- NA-08/13
*Chebfun: A New Kind of Numerical Computing*

R B Platte and L N Trefethen- NA-08/12
*Householder triangularization of a quasimatrix*

L N Trefethen- NA-08/11
*The chebop system for automatic solution of differential equations*

T Driscoll, F Bornemann and L N Trefethen- NA-08/10
*Optimal solvers for PDE-Constrained Optimization*

T Rees, H S Dollar and A J Wathen- NA-08/09
*A second derivative SQP method with imposed descent*

N I M Gould, D P Robinson- NA-08/08
*A Bramble-Pasciak-like method with applications in optimization*

H S Dollar, N I M Gould, M Stoll, and A J Wathen- NA-08/07
*Piecewise smooth chebfuns*

R Pachón, R Platte and L N Trefethen- NA-08/06
*GMRES for the differentiation operator*

S Olver- NA-08/05
*A Primal-Dual Augmented Lagrangian*

P E Gill, D P Robinson- NA-08/04
*A Sixth-Order Extension to the MATLAB Package bvp4c of J. Kierzenka and L. Shampine*

N Hale, D R Moore- NA-08/03
*A Krylov-Schur approach to the truncated SVD*

M Stoll- NA-08/02
*Trust-region and other regularisations of linear least-squares problems*

C Cartis, N I M Gould and P L Toint- NA-08/01
*An extended collection of matrix derivative results for forward and reverse mode automatic differentiation*

M Giles

**2007**

- NA-07/22
*Approximation of the scattering amplitude*

G H Golub, M Stoll and A Wathen- NA-07/21
*Linear instability of asymmetric Poiseuille flows*

D Kachuma, I Sobey- NA-07/20
*Adaptive cubic overestimation methods for unconstrained optimization*

C Cartis, N I M Gould and P L Toint- NA-07/19
*Numerical approximation of corotational dumbbell models for dilute polymers*

J W Barrett, E Süli- NA-07/18
*Kalman Filtering with Equality and Inequality State Constraints*

N Gupta, R Hauser- NA-07/17
*Computing***A**^{α}, log(**A**) and related matrix functions by contour integrals

N Hale, N J Higham, L N Trefethen- NA-07/16
*Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift*

D Knezevic, E Süli- NA-07/15
*New quadrature formulas from conformal maps*

N Hale, L N Trefethen- NA-07/14
*Kalman filtering in the presence of State Space Equality Constraints*

N Gupta- NA-07/13
*The Bramble-Pasciak preconditioner for saddle point problems*

M Stoll, A Wathen- NA-07/12
*Monte Carlo evaluation of sensitivities in computational finance*

M Giles- NA-07/11
*Combination preconditioning and self-adjointness in non-standard inner products with application to saddle point problems*

M Stoll, A Wathen- NA-07/10
*Variational Convergence of IP-DGFEM*

A Buffa, C Ortner- NA-07/09
*Nonlinear programming without a penalty function or a filter*

N I M Gould, Ph L Toint- NA-07/07
*Preconditioning and convergence in the right norm*

A Wathen- NA-07/06
*A New Approach to Yakubovich's s-Lemma*

R Hauser- NA-07/05
*A new perspective on the complexity of interior point methods for linear programming*

C Cartis, R Hauser- NA-07/04
*Sparse finite element approximation of high-dimensional transport-dominated diffusion problems*

C Schwab, E Süli, RA Todor- NA-07/03
*Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method*

P Benner, H Faßbender, M Stoll- NA-07/02
*How good are projection methods for convex feasibility problems?*

N I M Gould- NA-07/01
*Finding a point in the relative interior of a polyhedron*

C Cartis, N I M Gould

**2006**

- NA-06/22
*Improved multilevel Monte Carlo convergence using the Milstein scheme*

M B Giles- NA-06/20
*Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals*

T Schmelzer, L N Trefethen- NA-06/19
*Finite element methods for deterministic simulation of polymeric fluids*

D Knezevic- NA-06/18
*A Gagliardo-Nirenberg inequality, with application to duality-based a posteriori error estimation in the L*^{1}norm

E Süli- NA-06/17
*Summing curious, slowly convergent, harmonic subseries*

T Schmelzer, R Baillie- NA-06/16
*The Kink Phenomenon in Fejér and Clenshaw-Curtis Quadrature*

J A C Weideman, L N Trefethen- NA-06/15
*A-posteriori error analysis of hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic problems*

P Houston, E Süli, T P Wihler- NA-06/14
*Existence of global weak solutions to kinetic models for dilute polymers*

J W Barrett, E Süli- NA-06/13
*A-posteriori analysis and adaptive algorithms for the quasicontinuum method in one dimension*

C Ortner, E Süli- NA-06/12
*A-priori analysis of the quasicontinuum method in one dimension*

C Ortner, E Süli- NA-06/11
*A-posteriori existence in adaptive computations*

C Ortner- NA-06/10
*Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows*

S Berrone, E Süli- NA-06/09
*Deducing the multi-trader population driving a financial market*

N Gupta, R Hauser, N F Johnson- NA-06/08
*A DC-programming algorithm for kernel selection*

A Argyriou, R Hauser, C A Micchelli, M Pontil- NA-06/07
*Is Gauss quadrature better than Clenshaw-Curtis?*

L N Trefethen- NA-06/06
*Numerical Analysis*

L N Trefethen- NA-06/05
*Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems*

C Ortner, E Süli- NA-06/04
*On pseudospectra and power growth*

T Ransford- NA-06/03
*Multi-level Monte Carlo path simulation*

M B Giles- NA-06/02
*Some preconditioning techniques for saddle point problems*

M Benzi, A J Wathen- NA-06/01
*Algebraic tail decay of condition numbers for random conic systems under a general family of input distributions*

R Hauser, T Müller

**2005**

- NA-05/30
*Approximation to the mean curve in the LCS problem*

C Durringer, R Hauser, H Matzinger- NA-05/29
*Parabolic and hyperbolic contours for computing the Bromwich integral*

J A C Weideman, L N Trefethen- NA-05/28
*Taming a Hydra of Singularities*

F Bornemann, T Schmelzer- NA-05/27
*Computing the Gamma function using contour integrals and rational approximations*

T Schmelzer, L N Trefethen- NA-05/26
*Updating the QR decomposition of block tridiagonal and block Hessenberg matrices generated by block Krylov space methods*

M H Gutknecht, T Schmelzer- NA-05/25
*Using automatic differentiation for adjoint CFD code development*

M B Giles, D Ghate, M C Duta- NA-05/24
*Efficient agent-based models for non-genomic evolution*

N Gupta, A Agogino, K Turner- NA-05/23
*Using contstraint preconditioners with regularized saddle-point problems*

H S Dollar, N I M Gould, W H A Schilders, A J Wathen- NA-05/22
*A rational spectral collocation method with adaptively transformed Chebyshev grid points*

T W Tee, L N Trefethen- NA-05/21
*MMPDE vs SGWMFE Experiments in one dimension*

A Wacher- NA-05/20
*Talbot quadratures and rational approximations*

L N Trefethen, J A C Weideman, T Schmelzer- NA-05/19
*Finite element approximation of high-dimensional transport-dominated diffusion problems*

E Süli- NA-05/18
*On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems*

H Sue Dollar, Nicholas I M Gould, Wil H A Schilders, Andrew J Wathen- NA-05/17
*Sharp error estimates for discretisations of the 1D convection/diffusion equation with Dirac initial data*

R Carter, M B Giles- NA-05/16
*Convergence analysis of Crank-Nicolson and Rannacher time-marching*

M B Giles, R Carter- NA-05/15
*Smoking adjoints: fast evaluation of Greeks in Monte Carlo calculations*

M B Giles, P Glasserman- NA-05/14
*Computed eigenmodes of planar regions*

L N Trefethen and T Betcke- NA-05/13
*Ten Digit Algorithms*

L N Trefethen- NA-05/12
*A note on the design hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems*

E H Georgoulis, A Lasis- NA-05/11
*Continuum limit of a one-dimensional atomistic energy based on local minimization*

C Ortner- NA-05/10
*Two variational techniques for the approximation of curves of maximal slope*

C Ortner- NA-05/09
*Forecasting financial time series using artificial market models*

N Gupta, R Hauser, N F Johnson- NA-05/08
*Local uniqueness of alignments with a fixed proportion of gaps*

R Hauser, H Matzinger- NA-05/07
*On the discontinuous Galerkin method for Friedrichs systems in graph spaces*

M Jensen- NA-05/06
*Some new results concerning the primal-dual path-following interior point algorithm for linear programming*

C Cartis- NA-05/05
*Optimizing Talbot's contours for the inversion of the Laplace transform.*

J A C Weideman- NA-05/04
*On the convergence of a primal-dual second-order corrector interior point algorithm for linear programming*

C Cartis- NA-05/03
*A randomized algorithm for the MaxFS problem*

E Amaldi, P Belotti, R Hauser- NA-05/02
*Extending constraint preconditioners for saddle point problems*

H S Dollar- NA-05/01
*Preconditioning harmonic unsteady potential flow calculations*

A L Laird, M B Giles

**2004**

- NA-04/29
*Some equivalent characterisations of the polynomial numerical hull of degree k*

J Burke, A Greenbaum- NA-04/28
*On implicit-factorisation constraint preconditioners*

H S Dollar, N I M Gould, A J Wathen- NA-04/27
*Some disadvantages of a Mehrotra-type promal-dual corrector interior point algorithm for linear programming*

C Cartis- NA-04/26
*$\Gamma$-Limits of Galerkin Discretisations with Quadrature*

C Ortner- NA-04/25
*One-parameter discontinuous Galerkin finite element discretisation of quasilinear parabolic problems*

A Lasis, E Süli- NA-04/24
*Stabilization mechanisms in discontinuous Galerkin finite element methods*

F Brezzi, B Cockburn, D Marini, E Süli- NA-04/23
*A-posteriori error estimators and RFB*

A Cangiani, E Süli- NA-04/22
*Existence of global weak solutions for some polymeric flow models*

J W Barrett, Ch Schwab, E Süli- NA-04/21
*Finite element solution of a membrane covered electrode problem*

K Harriman, D Gavaghan, E Süli- NA-04/20
*Application of hpDGFEM to mechanisms at channel microband electrodes*

K Harriman, D Gavaghan, E Süli- NA-04/19
*Approximation of linear functionals using an hp-adaptive discontinuous Galerkin finite element method*

K Harriman, D Gavaghan, E Süli- NA-04/18
*The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method*

K Harriman, D Gavaghan, E Süli- NA-04/17
*Sharp error estimates for a discretisation of the 1D convection/diffusion equation with Dirac initial data*

M B Giles- NA-04/16
*Computed tomography from X-rays: old 2-D results, new 3-D problems*

K Miller- NA-04/15
*Computations of eigenvalue avoidance in planar domains*

T Betcke, L N Trefethen- NA-04/14
*Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case*

P Houston, J A Robson, E Süli- NA-04/13
*A posteriori error analysis of mixed finite element approximations to quasi-Newtonian incompressible flows*

J W Barrett, J A Robson, E Süli- NA-04/12
*Time and space adaptivity for the second-order wave equation*

C Bernardi, E Süli- NA-04/11
*Eigenmode analysis for turbomachinery applications*

P Moinier, M B Giles- NA-04/10
*On the relationship between convergence rates of discrete and continuous dynamical systems*

R Hauser, J Nedic- NA-04/09
*Spectral method for unsteady incompressible Navier-Stokes equations in gauge formulation*

T W Tee, I J Sobey- NA-04/08
*Preconditioning and fast solvers for incompressible flow*

A J Wathen- NA-04/07
*Wave packet pseudomodes of variable coefficient differential operators*

L N Trefethen- NA-04/06
*A solenoidal finite element approach for prediction of radar cross-sections*

A N F Mack- NA-04/05
*hp-version interior penalty DGFEMs for the biharmonic equation*

I Mozolevski, E Süli- NA-04/04
*A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains*

A Madzvamuse, P K Maini, A J Wathen- NA-04/03
*A hydro-elastic model of hydrocephalus*

A Smillie, I Sobey and Z Molnar- NA-04/02
*Discontinuous Galerkin methods for first-order hyperbolic problems*

F Brezzi, L D Marini, E Süli- NA-04/01
*Incomplete factorization constraint preconditioners for saddle-point matrices*

H S Dollar, A J Wathen

**2003**

- NA-03/18
*Boundedness theorems for the relaxation method*

E Amaldi, R Hauser- NA-03/17
*Enhanced RFB method*

A Cangiani, E Süli- NA-03/16
*Solving reaction-diffusion equations 10 times faster*

A-K Kassam- NA-03/15
*String gradient weighted moving finite elements for systems of partial differential equations*

A Wacher, I Sobey, K Miller- NA-03/14
*Fourth-order time stepping for stiff PDEs*

A-K Kassam, L N Trefethen- NA-03/13
*Large deviation based upper bounds for the LCS-problem*

R Hauser, S Martinez, H Matzinger- NA-03/12
*Reviving the method of particular solutions*

T Betcke, L N Trefethen- NA-03/11
*hp-Version discontinuous Galerkin finite element methods for semilinear parabolic problems*

A Lasis, E Süli- NA-03/10
*Poincaré-type inequalities for broken Sobolev spaces*

A Lasis, E Süli- NA-03/09
*Sparse approximate inverses and target matrices*

R M Holland, A J Wathen, G J Shaw- NA-03/08
*On tail decay and moment estimates of a condition number for random linear conic systems*

D Cheung, F Cucker, R Hauser- NA-03/06
*Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method*

E H Georgoulis and E Süli- NA-03/05
*The continuous Newton-Raphson method can look ahead*

R Hauser, J Nedic- NA-03/04 - not available electronically
*Block Smoothed Aggregation AMG Preconditioning for Oil Reservoir Simulation Systems*

A T Papadopoulos, H Tchelepi- NA-03/03
*An extension of MATLAB to continuous functions and operators*

Z Battles, L N Trefethen- NA-03/02
*Pigmentation Pattern Formation in Butterflies - Experiments and Models -*

F H Nijhout, P K Maini, A Madzvamuse, A J Wathen, T Sekimura- NA-03/01
*The Nesterov-Todd direction and its relation to weighted analytic centers*

R Hauser

**2002**

- NA-02/22
*Wave packet pseudomodes of twisted Toeplitz matrices*

L N Trefethen, S J Chapman- NA-02/21
*hp-Version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form*

K Harriman, P Houston, B Senior, E Süli- NA-02/20
*A moving grid finite element method applied to a model biological pattern generator*

A Madzvamuse, A J Wathen, P K Maini- NA-02/19
*The moving grid finite element method applied to biological problems*

A Madzvamuse, R D K Thomas, T Sekimura, A J Wathen, P K Maini- NA-02/18
*Pigmentation pattern formation in the butterfly wing of Papilio dardanus*

T Sekimura, A Madzvamuse, A J Wathen, P K Maini- NA-02/17
*Implications of domain growth in morphogenesis*

P K Maini, E J Crampin, A Madzvamuse, A J Wathen, R D K Thomas- NA-02/16
*Barycentric Lagrange Interpolation*

J-P Berrut and L N Trefethen- NA-02/15
*Limited memory solution of complementarity problems arising in video games*

M C Ferris and A J Wathen- NA-02/14
*A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides*

L Banjai and L N Trefethen- NA-02/13
*Analysis of preconditioners for saddle-point problems*

D Loghin and A J Wathen- NA-02/12
*Preconditioned iterative solution of the 2D Helmholtz equation*

A L Laird and M B Giles- NA-02/11
*Mathematical programs with equilibrium constraints: automatic reformulation and solution via constrained optimization*

M C Ferris, S P Dirkse and A Meeraus- NA-02/10
*Discrete adjoint approximations with shocks*

M B Giles- NA-02/09
*Linearized pipe flow to Reynolds number 10*^{7}

Á Meseguer and L N Trefethen- NA-02/08
*A predictive model for color pattern formation in the butterfly wing of Papilio dardanus*

A Madzvamuse, P K Maini, A J Wathen, T Sekimura- NA-02/07
*Incomplete orthogonal factorization methods using Givens Rotations II: implementation and results*

A T Papadopoulos, I S Duff, A J Wathen- NA-02/06
*Neuro-dynamic programming for radiation treatment planning*

M C Ferris, M M Voelker- NA-02/05
*Density and trace for graph spaces of first-order linear operators*

M Jensen- NA-02/04
*A preconditioner for the 3D Oseen equations*

A Wathen, D Loghin, D Kay, H Elman, D Silvester- NA-02/03
*A new perspective on the stability of unsteady stream-function voriticity calculations*

E Sousa, I J Sobey- NA-02/02
*Sobolev regularity estimation for hp-adaptive finite element methods*

P Houston, B Senior, E Süli- NA-02/01
*Adaptive finite element approximation of hyperbolic problems*

E Süli, P Houston

**2001**

- NA-01/23
*Numerical solution of the omitted area problem of univalent function theory*

L Banjai, L N Trefethen- NA-01/22
*The Tortoise and the Hare restart GMRES*

M Embree- NA-01/21
*Convergence of restarted Krylov subspaces to invariant subspaces*

C Beattie, M Embree, J Rossi- NA-01/20
*Schur complement preconditioning for elliptic systems of partial differential equations*

D Loghin, A J Wathen- NA-01/19
*A spectral Petrov-Galerkin formulation for pipe flow II: Nonlinear transitional stages*

Á Meseguer and L N Trefethen- NA-01/18
*Adjoint error correction for integral outputs*

M B Giles, N A Pierce- NA-01/17
*A numerical approach to the study of spatial pattern formation in the ligaments of arcoid bivalves*

A Madzvamuse, R D K Thomas, P K Maini, A J Wathen- NA-01/16
*The spectra of large Toeplitz band matrices with a randomly perturbed entry*

A Böttcher, M Embree, V I Sokolov- NA-01/15
*Algorithm developments for discrete adjoint methods*

M B Giles, M C Duta, J-D Müller, N A Pierce- NA-01/14
*Analysis of adjoint error correction for superconvergent functional estimates*

M B Giles, N A Pierce- NA-01/13
*Eigenvalues and pseudospectra of rectangular matrices*

T G Wright, L N Trefethen- NA-01/12
*Nonnormal energy transient growth in the Taylor-Couette problem*

Á Meseguer- NA-01/11
*A family of finite difference schemes for the convection-diffusion equation in two dimensions*

E Sousa, I J Sobey- NA-01/10
*Analysis of preconditioned Picard iterations for the Navier-Stokes equations*

D Loghin- NA-01/09
*hp-DGFEM on shape-irregular meshes: reaction-diffusion problems*

E H Georgoulis, E Süli- NA-01/08
*On large Toeplitz matrices with an uncertain block*

A Böttcher, M Embree, V I Sokolov- NA-01/07
*hp-Discontinuous Galerkin finite element methods for problems: error analysis and adaptivity*

E Süli, P Houston, B Senior- NA-01/06
*Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic problems*

P Houston, R Hartmann, E Süli- NA-01/05
*hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems*

P Houston, E Süli- NA-01/04
*Variational approximation of flux in conforming finite element methods for elliptic partial differential equations: a model problem*

F Brezzi, T J R Hughes, E Süli- NA-01/03
*Enhanced accuracy by post-processing for finite element methods for hyperbolic equations*

B Cockburn, M Luskin, C-W Shu, E Süli- NA-01/02
*Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes*

P Moinier, M B Giles- NA-01/01
*Spectral approximation of banded Laurent matrices with localized random perturbations*

A Böttcher, M Embree, M Lindner

**2000**

- NA-00/22
*The reliability of local error estimators for convection-diffusion equations*

D Kay and D Silvester- NA-00/21
*Understanding MA27 - A Numerical Example*

C Keller- NA-00/20
*Flutter and Forced Response of Mistuned Turbomachinery*

M S Campobasso and M B Giles- NA-00/19
*Piecewise continuous Toeplitz matrices and operators: slow approach to infinity*

A Böttcher, M Embree, L N Trefethen- NA-00/18
*A spectral Petrov-Galerkin formulation for pipe flow I: Linear stability and transient growth*

Á Meseguer and L N Trefethen- NA-00/17
*Threshold amplitudes for transition to turbulence in a pipe*

L N Trefethen, S J Chapman, D S Henningson, Á Meseguer, T Mullin and F T M Nieuwstadt- NA-00/16
*Infinite Toeplitz and Laurent matrices with localized impurities*

A Böttcher, M Embree, V I Sokolov- NA-00/15
*Discontinuous hp-finite element methods for advection-diffusion problems*

P Houston, Ch Schwab and E Süli- NA-00/14
*An abstract formulation of the concept of entropy*

J D P Donnelly- NA-00/13
*Preconditioned iterative methods for implicit equations*

A J Wathen- NA-00/12
*Generalizing eigenvalue theorems to pseudospectra theorems.*

M Embree and L N Trefethen- NA-00/11
*Large-scale computation of pseudospectra using ARPACK and eigs.*

T G Wright and L N Trefethen- NA-00/10
*On the use of Runge-Kutta time-marching and multigrid for the solution of steady adjoint equations.*

M B Giles- NA-00/09
*Adaptive finite element simulation of currents at microelectrodes to a guaranteed accuracy. Accuracy to channel microband electrodes.*

K Harriman, D Gavaghan, P Houston, D Kay and E Süli- NA-00/08
*The influence of unstructured mesh type on the prediction of convoluted shear layers*

H Salman, J J McGuirk, G J Page and P Moinier- NA-00/07
*Spectra, pseudospectra and localization for random bidiagonal matrices*

L N Trefethen, M Contedini and M Embree- NA-00/06
*A model for colour pattern formation in the butterfly wing of Papilio dardanus*

T Sekimura, A Madzvamuse, A J Wathen and P K Maini- NA-00/05
*Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations*

D L Darmofal, P Moinier and M B Giles- NA-00/04
*An introduction to the adjoint approach to design*

M B Giles and N A Pierce- NA-00/03
*Analytic adjoint solutions for the quasi-1D Euler equations*

M B Giles and N A Pierce- NA-00/02
*Improved lift and drag estimates using adjoint Euler equations*

M B Giles and N A Pierce- NA-00/01
*Computing Lyapunov constants for random recurrences with smooth coefficients*

T G Wright and L N Trefethen

**1999**

- NA-99/20
*A robust a posteriori estimator for the residual-free bubbles method applied to advection-diffusion problems*

G Sangalli- NA-99/19
*Adaptive Finite Element Simulation of Steady State Currents at Microdisc Electrodes to a Guaranteed Accuracy*

K Harriman, D Gavaghan, P Houston and E Süli- NA-99/18
*Stabilized hp-Finite Element Approximation of Partial Differential Equations with Nonnegative Characteristic Form*

P Houston and E Süli- NA-99/17
*Efficient preconditioning of the linearized Navier-Stokes equations*

D Silvester, H Elman, D Kay and A Wathen- NA-99/16
*On dynamic computational subgrid modeling*

J Hoffman and C Johnson- NA-99/15
*A nearly optimal preconditioner for the Navier-Stokes equations*

L Hemmingsson-Franden and A Wathen- NA-99/14
*Modeling Subgrid Viscosity for Advection--Diffusion Problems*

F Brezzi, P Houston, D Marini and E Süli- NA-99/13
*A class of incomplete orthogonal factorization methods. I: methods and theories*

Z-Z Bai, I S Duff, A J Wathen- NA-99/11
*hp-Finite Element Methods for Hyperbolic Problems*

E Süli, P Houston, Ch Schwab- NA-99/09
*A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation*

E Süli, C Wilkins- NA-99/08
*How descriptive are GMRES convergence bounds?*

M Embree- NA-99/07
*A note on preconditioning for indefinite linear systems*

M F Murphy, G H Golub, A J Wathen- NA-99/06
*A Green's function preconditioner for the steady-state Navier-Stokes equations*

D Kay, D Loghin- NA-99/04
*A posteriori error analysis for stabilised finite element approximations of transport problems*

P Houston, R Rannacher, E Süli- NA-99/03
*Computation of Pseudospectra*

L N Trefethen- NA-99/02
*hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form*

E Süli, Ch Schwab, P Houston- NA-99/01
*Constraint preconditioning for indefinite linear systems*

C Keller, N I M Gould, A J Wathen

**1998**

- NA-98/21
*Green's functions for multiply connected domains via conformal mapping*

M Embree, L N Trefethen- NA-98/20
*Multi-Adaptive Error Control for ODEs*

A Logg- NA-98/19 - not available electronically
*The potential theory of several intervals and its applications*

J Shen, G Strang, A J Wathen- NA-98/18
*Adjoint recovery of superconvergent functionals from approximate solutions of partial differential equations*

N A Pierce, M B Giles- NA-98/17 - not available electronically
*Evolution Galerkin methods as finite difference schemes*

K W Morton- NA-98/16
*Finite difference approximation of a convection diffusion equation near a boundary*

E Sousa, I J Sobey- NA-98/15
*Stiff oscillatory systems, delta jumps and white noise*

B Cano, A M Stuart, E Süli, J O Warren- NA-98/14
*Stabilized hp-finite element methods for first-order hyperbolic problems*

P Houston, C Schwab, E Süli- NA-98/13 - not available electronically
*Deploying fault tolerance and task migration with NetSolve*

J S Plank, H Casanova, M Beck, J Dongarra- NA-98/12
*Predictions for Scientific Computing Fifty Years from Now*

L N Trefethen- NA-98/11
*Residual-free bubbles for advection-diffusion problems: the general error analysis*

Franco Brezzi, Donatella Marini, Endre Süli- NA-98/10 - not available electronically
*Analysis and experiments for a computational model of a heat bath*

A M Stuart, J O Warren- NA-98/09 - not available electronically
*How many shuffles to randomize a deck of cards?*

Lloyd N Trefethen, Lloyd M Trefethen- NA-98/08 - not available electronically
*Schwarz-Christoffel Mapping in the Computer Era*

Lloyd N Trefethen, Tobin A Driscoll- NA-98/07 - not available electronically
*A priori error analysis of a finite element method with residual-free bubbles for advection dominated equations*

Franco Brezzi, T J R Hughes, Donatella Marini, Alessandro Russo and Endre Süli- NA-98/05 - not available electronically
*Smooth Numerical Representation of the Motion of Two Linked Rigid Rods in R*^{2}and R^{3}

F S Chaudhry, D C Handscomb- NA-98/04 - not available electronically
*Smooth Motion of a Rigid Triangle in R*^{2}

F S Chaudhry, D C Handscomb- NA-98/03
*Decay of the total variation and Hardy norms of solutions to parabolic conservation laws*

Maria Elena Schonbek and Endre Süli- NA-98/02
*The adaptive computation of far-field patterns by a posteriori estimation of linear functionals*

Peter Monk and Endre Süli- NA-98/01
*Computation of Deterministic Volatility Surfaces*

Nicolas Jackson, Endre Süli, Sam Howison

**1997**

- NA-97/22 - not available electronically
*The Random Recurrence x*_{n+1}= x_{n}± bx_{n-1}

Mark Embree and Lloyd N Trefethen- NA-97/21
*A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems*

E Süli- NA-97/20
*Eigenvalues and Musical Instruments*

V E Howle and Lloyd N Trefethen- NA-97/19 - not available electronically
*Smooth motion of a rigid rod in R*^{3}

F S Chaudhry and D C Handscomb- NA-97/18 - not available electronically
*Smooth motion of a rigid rod in R*^{2}

F S Chaudhry and D C Handscomb- NA-97/17 - not available electronically
*Random Fibonacci Sequences and the Number 1.13198824 ...*

D Viswanath- NA-97/16
*The convergence of iterative solution methods for symmetric and indefinite linear systems*

A J Wathen, B Fischer and D J Silvester- NA-97/15
*Preconditioning the Advection-Diffusion Equation: the Green's Function Approach*

D Loghin and A J Wathen- NA-97/14 - not available electronically
*A Posteriori Error Indicators for Hyperbolic Problems*

Paul Houston and Endre Süli- NA-97/13 - not available electronically
*The Kreiss Matrix Theorem on a General Complex Domain*

Kim-Chuan Toh and Lloyd N Trefethen- NA-97/12
*A Numerical Analyst Looks at the "Cutoff Phenomenon" in Card Shuffling and Other Markov Chains*

Gudbjorn F Jonsson and Lloyd N Trefethen- NA-97/11
*On adjoint equations for error analysis and optimal grid adaptation in CFD*

M B Giles- NA-97/10 - not available electronically
*Stabilised finite element methods for steady incompressible flow*

Henrik Blank, Michael Rudgyard and Andrew Wathen- NA-97/09 - not available electronically
*Theoretical and computational mechanics of a flexible cable*

David Handscomb- NA-97/08
*Aerodynamic design optimisation for complex geometries using unstructured grids*

M B Giles- NA-97/07
*Aerospace design: a complex task*

M B Giles- NA-97/06
*Adaptive error control for finite element approximations of the lift and drag coefficients in viscous flow*

Michael Giles, Mats G Larson, J Marten Levenstam and Endre Süli- NA-97/05
*Adaptive Finite Element Solution of 1D European Option Pricing Problems*

Nicholas Jackson and Endre Süli- NA-97/04
*A Posteriori Error Analysis for Systems of Nonlinear Convection-Diffusion Equations*

Paul Houston and Endre Süli- NA-97/03
*A Posteriori Error Analysis for Linear Convection-Diffusion Problems Under Weak Mesh Regularity Assumptions*

Paul Houston and Endre Süli- NA-97/02 - not available electronically
*A Semi-circulant Preconditioner for the Convection-Diffusion Equation*

L Hemmingsson- NA-97/01 - not available electronically
*On the analysis of finite volume methods for evolutionary problems*

K W Morton

**1996**

- NA-96/27 - not available electronically
*L(infinity) estimates on the solutions of non-selfadjoint elliptic and parabolic equations in bounded domains*

A T Hill- NA-96/25 - not available electronically
*Analysis of finite element time domain methods in electromagnetic scattering*

P Monk, A K Parrott and A Le Hyaric- NA-96/24 - not available electronically
*Simulations of order transitions on a parallel computer*

D C Handscomb- NA-96/23 - not available electronically
*Adaptive finite element methods for the damped wave equation*

E Süli and C Wilkins- NA-96/22 - not available electronically
*Attractors for a second-order approximation of the incompressible Navier-Stokes equations in two space dimensions*

A T Hill and E Süli- NA-96/21 - not available electronically
*The stability of boundary conditions for an angled-derivative difference scheme*

K W Morton and N A Burgess- NA-96/20 - not available electronically
*Recent developments in evolution-Galerkin methods*

K W Morton- NA-96/19
*Iterative Methods for Problems in Computational Fluid Dynamics*

H Elman, D Silvester and A Wathen- NA-96/18
*Mixing Calculations in a Rotating Partitioned Pipe*

C Glasgow and A K Parrott- NA-96/17 - not available electronically
*A BSP Approach to Dynamic Load Balancing Using a Constrained Diffusion Algorithm*

R Burrows and A K Parrott- NA-96/16 - not available electronically
*The multigrid solution of two-factor American put options*

N Clarke and A K Parrott- NA-96/14
*Fractal Characteristics of Newton's Method on Polynomials*

M Drexler, I Sobey and C Bracher- NA-96/13 - not available electronically
*Approximation of multidimensional hyperbolic partial differential equations*

K W Morton- NA-96/11 - not available electronically
*Bulk Synchronous Parallelisation of Industrial Magnetic Software*

M C Dracopoulos, C Glasgow, A K Parrott and J Simpkin- NA-96/09
*Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity*

Endre Süli and Paul Houston- NA-96/08 - not available electronically
*Artificial viscosity for the cell vertex method*

S M Stringer and K W Morton- NA-96/07
*On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids*

P Houston and E Süli- NA-96/06
*Stability and convergence of discretisations of initial value PDEs*

M B Giles- NA-96/05
*Particle tracking methods for residence time calculations in incompressible flow*

C Glasgow, A K Parrott and D C Handscomb- NA-96/04
*Multiple knot B-spline representation of incompressible flow*

C Glasgow, A K Parrott and D C Handscomb- NA-96/03
*The theory, practice, and a tool for BSP performance prediction applied to a CFD application*

Jonathan M D Hill, Paul I Crumpton and David A Burgess- NA-96/02
*Coercivity for One-dimensional Cell Vertex Approximations*

K W Morton- NA-96/01
*Diagonal Dominance and Positive Definiteness of Upwind Approximations for Advection Diffusion Problems*

G Golub, D Silvester, A Wathen

**1995**

- NA-95/26
*On the fractal characteristics of a stabilised Newton method*

M Drexler, I J Sobey, C Bracher- NA-95/25 - not available electronically
*Genuinely high-resolution conservative algorithms for two-dimensional advection*

P Lin, K W Morton, E Süli- NA-95/24
*Adaptive Lagrange-Galerkin methods for unsteady convection-dominated diffusion problems*

P Houston and E Süli- NA-95/23
*Multiresolution and wavelets*

D C Handscomb- NA-95/22 - not available electronically
*The adaptive CCCG(eta) method for efficient solution of time dependent partial differential equations*

F F Campos, N R C Birkett- NA-95/21 - not available electronically
*Parallel visulations of unstructured grids*

P I Crumpton, R Haimes- NA-95/20
*A parallel framework for unstructured grid solvers*

D A Burgess, P I Crumpton, M B Giles- NA-95/19
*An efficient cell vertex method for unstructured tetrahedral grids*

P I Crumpton- NA-95/18
*Aircraft computations using multigrid and an unstructured parallel library*

P I Crumpton, M B Giles- NA-95/17
*Implicit time accurate solutions on unstructured dynamic grids*

P I Crumpton, M B Giles- NA-95/16 - not available electronically
*Absorbing boundary conditions for the reduced wave equation*

J D P Donnelly- NA-95/15 - not available electronically
*Finite Volume Methods for CFD*

K W Morton- NA-95/14 - not available electronically
*A posteriori error analysis and global error control for adaptive finite element approximations of hyperbolic problems*

E Süli- NA-95/13
*Stability and accuracy of numerical boundary conditions in aeroelastic analysis*

M B Giles- NA-95/12
*Stability analysis of numerical interface boundary conditions for parabolic equations*

M B Giles- NA-95/11 - not available electronically
*A posteriori error estimation based on discrepancies in an entropy variable*

J G Andrews, K W Morton- NA-95/10
*Preconditioning on stretched meshes*

N A Pierce, M B Giles- NA-95/09 - not available electronically
*Errors of linear interpolation on a triangle*

D C Handscomb- NA-95/08 - not available electronically
*Domain decomposition preconditioning*

K Terekhova, D F Mayers- NA-95/07 - not available electronically
*Finite volume methods for inviscid and viscous flows, steady and unsteady*

K W Morton, S M Stringer- NA-95/06 - not available electronically
*Renumbering unstructured grids to improve the performance of codes on hierarchical memory machines*

D A Burgess, M B Giles- NA-95/05 - not available electronically
*Controlled Cholesky factorisation for preconditioning the Conjugate Gradient method*

F F Campos, J S Rollett- NA-95/04
*Stability analysis of Galerkin/Runge-Kutta Navier-Stokes discretisations on unstructured grids*

M B Giles- NA-95/03
*Analysis of the accuracy of shock-capturing in the steady quasi-1D Euler equations*

M B Giles- NA-95/02 - not available electronically
*Godunov Type of the Euler Characteristic Galerkin Scheme for One Dimensional Scaler Conservation Laws*

P Lin- NA-95/01 - not available electronically
*A posteriori analysis of Petrov-Galerkin approximations of Friedrichs systems*

J A Mackenzie, E Süli, G Warnecke

- NA-13/26
*A frequency-independent boundary element method for scattering by two-dimensional screens and apertures*

D P Hewett, S Langdon and S N Chandler-Wilde- NA-13/25
*Acoustic scattering by fractal screens: mathematical formulations and wavenumber-explicit continuity and coercivity estimates*

S N Chandler-Wilde and D P Hewett- NA-13/24
*Well-balanced r-adaptive and moving mesh space-time discontinuous Galerkin method for the shallow water equations*

S Rhebergen- NA-13/23
*Efficient smoothers for all-at-once multigrid methods for Poisson and Stokes control problems*

S Takacs- NA-13/22
*Natural preconditioners for saddle point systems*

J Pestana and A J Wathen- NA-13/21
*The antitriangular factorisation of saddle point matrices*

J Pestana and A J Wathen- NA-13/20
*A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing*

C Cartis and A Thompson- NA-13/19
*Preconditioned iterative methods for Navier-Stokes control problems*

J W Pearson- NA-13/18
*On the role of commutator arguments in the development of parameter-robust preconditioners for Stokes control problems*

J W Pearson- NA-13/17
*A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions*

M Javed and L N Trefethen- NA-13/16
*A fast, simple, and stable Chebyshev-Legendre transform using an asymptotic formula*

N Hale and A Townsend- NA-13/15
*The exponentially convergent trapezoidal rule*

L N Trefethen and J A C Weideman- NA-13/14
*Numerical algorithms based on analytic function values at roots of unity*

A P Austin, P Kravanja and L N Trefethen- NA-13/13
*On non-overlapping domain decomposition preconditioners for discontinuous Galerkin finite element methods in H*^{2}-type norms

I Smears- NA-13/12
*Efficient high-order rational integration and deferred correction with equispaced data*

S Güttel and G Klein- NA-13/11
*A robust all-at-once multigrid method for the Stokes control problem*

S Takacs- NA-13/10
*A robust multigrid method for the time-dependent Stokes problem*

S Takacs- NA-13/09
*Fast Solvers for Cahn-Hilliard Inpainting*

J Bosch, D Kay, M Stoll and A J Wathen- NA-13/08
*Computing the common zeros of two bivariate functions via Bezout resultants*

Y Nakatsukasa, V Noferini and A Townsend- NA-13/07
*On the spectral distribution of kernel matrices related to radial basis functions*

A J Wathen and S Zhu- NA-13/06
*Relative Robust Portfolio Optimization*

R Hauser, V Krishnamurthy and R Tütüncü- NA-13/05
*Performance Comparisons of Greedy Algorithms in Compressed Sensing*

J D Blanchard and J Tanner- NA-13/04
*Automatic linearity detection*

A Birkisson and T Driscoll- NA-13/03
*Discontinuous Galerkin finite element approximation of Hamilton-Jacobi-Bellman equations with Cordès coefficients*

I Smears and E Süli- NA-13/02
*Gaussian elimination as an iterative algorithm*

A Townsend and L N Trefethen- NA-13/01
*An extension of Chebfun to two dimensions*

A Townsend and L N Trefethen