Computational Mathematics and Applications
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Thu, 24/04/2008 14:00 |
Prof Toby Driscoll (University of Delaware) |
Computational Mathematics and Applications  |
Comlab |
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Thu, 01/05/2008 14:00 |
Prof Nick Trefethen (Computing Laboratory, Oxford) |
Computational Mathematics and Applications |
Comlab |
| "Eigenvalue avoidance" or "level repulsion" refers to the tendency of eigenvalues of matrices or operators to be distinct rather than degenerate. The mathematics goes back to von Neumann and Wigner in 1929 and touches many subjects including numerical linear algebra, random matrix theory, chaotic dynamics, and number theory. This talk will be an informal illustrated discussion of various aspects of this phenomenon. | |||
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Thu, 08/05/2008 14:00 |
Prof Beresford Parlett (UC Berkeley) |
Computational Mathematics and Applications |
Comlab |
| The task is to compute orthogonal eigenvectors (without Gram-Schmidt) of symmetric tridiagonals for isolated clusters of close eigenvalues. We review an "old" method, the Submatrix method, and describe an extension which significantly enlarges the scope to include several mini-clusters within the given cluster. An essential feature is to find the envelope of the associated invariant subspace. | |||
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Thu, 15/05/2008 14:00 |
Dr Stefano Berrone (Polytechnic of Torino) |
Computational Mathematics and Applications |
Comlab |
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Thu, 22/05/2008 14:00 |
Dr Michiel Hochstenbach (Technical University Eindhoven) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
| The Jacobi-Davidson method, proposed by Sleijpen and Van der Vorst more than a decade ago, has been successfully used to numerically solve large matrix eigenvalue problems. In this talk we will give an introduction to and an overview of this method, and also point out some recent developments. | |||
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Thu, 29/05/2008 14:00 |
Prof Marco Marletta (Cardiff University) |
Computational Mathematics and Applications |
Comlab |
| Dirichlet to Neumann maps and their generalizations are exceptionally useful tools in the study of eigenvalue problems for ODEs and PDEs. They also have real physical significance through their occurrence in electrical impedance tomography, with applications to medical imagine, landmine detection and non-destructive testing. This talk will review some of the basic properties of Dirichlet to Neumann maps, some new abstract results which make it easier to use them for a wide variety of models, and some analytical/numerical results which depend on them, including detection and elimination of spectral pollution. | |||
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Thu, 05/06/2008 14:00 |
Prof François Glineur (Universite catholique de louvain) |
Computational Mathematics and Applications |
Comlab |
| Among optimization problems, convex problems form a special subset with two important and useful properties: (1) the existence of a strongly related dual problem that provides certified bounds and (2) the possibility to find an optimal solution using polynomial-time algorithms. In the first part of this talk, we will outline how the framework of conic optimization, which formulates structured convex problems using convex cones, facilitates the exploitation of those two properties. In the second part of this talk, we will introduce a specific cone (called the power cone) that allows the formulation of a large class of convex problems (including linear, quadratic, entropy, sum-of-norm and geometric optimization). For this class of problems, we present a primal-dual interior-point algorithm, which focuses on preserving the perfect symmetry between the primal and dual sides of the problem (arising from the self-duality of the power cone). | |||
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Thu, 12/06/2008 14:00 |
Dr Paul Dellar (OCIAM) |
Computational Mathematics and Applications |
Comlab |
