Forthcoming Seminars › Seminar Series

Computational Mathematics and Applications

Thu, 19/01/2012
14:00 		Dr Jennifer Scott (STFC, Rutherford Appleton Laboratory) Computational Mathematics and Applications Add to calendar Rutherford Appleton Laboratory, nr Didcot
Antibandwidth maximization: a graph colouring problem
Thu, 26/01/2012
14:00 		Dr Andreas Grothey (University of Edinburgh) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Interior Point warmstarts and stochastic programming
We present progress on an Interior Point based multi-step solution approach for stochastic programming problems. Our approach works with a series of scenario trees that can be seen as successively more accurate discretizations of an underlying probability distribution and employs IPM warmstarts to "lift" approximate solutions from one tree to the next larger tree.
Thu, 02/02/2012
14:00 		Dr Coralia Cartis (University of Edinburgh) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Optimal Newton-type methods for nonconvex smooth optimization
We show that the steepest-descent and Newton's methods for unconstrained nonconvex optimization under standard assumptions may both require a number of iterations and function evaluations arbitrarily close to the steepest-descent's global worst-case complexity bound. This implies that the latter upper bound is essentially tight for steepest descent and that Newton's method may be as slow as the steepest-descent method in the worst case. Then the cubic regularization of Newton's method (Griewank (1981), Nesterov & Polyak (2006)) is considered and extended to large-scale problems, while preserving the same order of its improved worst-case complexity (by comparison to that of steepest-descent); this improved worst-case bound is also shown to be tight. We further show that the cubic regularization approach is, in fact, optimal from a worst-case complexity point of view amongst a wide class of second-order methods. The worst-case problem-evaluation complexity of constrained optimization will also be discussed. This is joint work with Nick Gould (Rutherford Appleton Laboratory, UK) and Philippe Toint (University of Namur, Belgium).
Thu, 09/02/2012
14:00 		Dr Yuji Nakatsukasa (University of Manchester) Computational Mathematics and Applications Add to calendar Rutherford Appleton Laboratory, nr Didcot
Efficient, communication-minimizing algorithms for the symmetric eigenvalue decomposition and the singular value decomposition
Computing the eigenvalue decomposition of a symmetric matrix and the singular value decomposition of a general matrix are two of the central tasks in numerical linear algebra. There has been much recent work in the development of linear algebra algorithms that minimize communication cost. However, the reduction in communication cost sometimes comes at the expense of significantly more arithmetic and potential instability.

In this talk I will describe algorithms for the two decompositions that have optimal communication cost and arithmetic cost within a small factor of those for the best known algorithms. The key idea is to use the best rational approximation of the sign function, which lets the algorithm converge in just two steps. The algorithms are backward stable and easily parallelizable. Preliminary numerical experiments demonstrate their efficiency.
Thu, 16/02/2012
14:00 		Professor Spencer Sherwin (Imperial College London) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
From h to p efficiently: balancing high or low order approximations with accuracy
Thu, 23/02/2012
14:00 		Dr Stephen Langdon (University of Reading) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
High frequency scattering by non-convex polygons
Standard numerical schemes for acoustic scattering problems suffer from the restriction that the number of degrees of freedom required to achieve a prescribed level of accuracy must grow at least linearly with respect to frequency in order to maintain accuracy as frequency increases. In this talk, we review recent progress on the development and analysis of hybrid numerical-asymptotic boundary integral equation methods for these problems. The key idea of this approach is to form an ansatz for the solution based on knowledge of the high frequency asymptotics, allowing one to achieve any required accuracy via the approximation of only (in many cases provably) non-oscillatory functions. In particular, we discuss very recent work extending these ideas for the first time to non-convex scatterers.
Thu, 01/03/2012
14:00 		Professor Paul Houston (University of Nottingham) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Two-Grid hp-Adaptive Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic PDEs
In this talk we present an overview of some recent developments concerning the a posteriori error analysis and adaptive mesh design of $ h $- and $ hp $-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems. In particular, we consider the derivation of computable bounds on the error measured in terms of an appropriate (mesh-dependent) energy norm in the case when a two-grid approximation is employed. In this setting, the fully nonlinear problem is first computed on a coarse finite element space $ V_{H,P} $. The resulting 'coarse' numerical solution is then exploited to provide the necessary data needed to linearise the underlying discretization on the finer space $ V_{h,p} $; thereby, only a linear system of equations is solved on the richer space $ V_{h,p} $. Here, an adaptive $ hp $-refinement algorithm is proposed which automatically selects the local mesh size and local polynomial degrees on both the coarse and fine spaces $ V_{H,P} $ and $ V_{h,p} $, respectively. Numerical experiments confirming the reliability and efficiency of the proposed mesh refinement algorithm are presented.
Thu, 08/03/2012
14:00 		Professor Rosie Renaut (Arizona State University) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Solution of ill-posed inverse problems pertaining to signal restoration
In this talk I review the use of the spectral decomposition for understanding the solution of ill-posed inverse problems. It is immediate to see that regularization is needed in order to find stable solutions. These solutions, however, do not typically allow reconstruction of signal features such as edges. Generalized regularization assists but is still insufficient and methods of total variation are commonly suggested as an alternative. In the talk I consider application of standard approaches from Tikhonov regularization for finding appropriate regularization parameters in the total variation augmented Lagrangian implementations. Areas for future research will be considered.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

Syndicate content