Program

Monday, September 21, 2015
morning
08:50 - 09:00
Welcoming Remarks
09:00 - 09:45
Sergey Dolgov (Max Planck Institute for Dynamics of complex technical systems, Magdeburg (D))
Alternating iteration for low-rank solution of linear systems with large indefinite matrices view abstract Sergey Dolgov
Alternating iteration for low-rank solution of linear systems with large indefinite matrices
High-dimensional partial differential equations arise naturally if spatial coordinates are extended by time and auxiliary variables. The latter may account for uncertain inputs or design parameters. After discretization, the number of degrees of freedom grows exponentially with the number of parameters. To reduce the complexity, we can employ the low-rank separation of variables and approximate large vectors and matrices by a polylinear combination of factors, each of whose depends only on one variable. One of the most powerful combinations are Tensor Train and Hierarchical Tucker decompositions. A workhorse method to compute the factors directly is the Alternating Least Squares iteration and its extensions. However, it was too difficult to treat matrices of a saddle point structure via existing alternating schemes. Such matrices occur in an optimal control problem, where a convex optimization, constrained by a high-dimensional PDE, is solved via Lagrangian approach. In this talk, we show how to preserve the saddle point structure of the linear system during the alternating iteration and solve it efficiently. We demonstrate numerical examples of the inverse Stokes-Brinkman and Navier-Stokes problems.
09:45 - 10:10
Boris Khoromskij (Max Planck Institute for Mathematics in the Sciences)
Towards numerical multi-linear algebra in logarithmic complexity
10:10 - 10:40
Coffee Break
10:40 - 11:05
Mike Espig (RWTH Aachen University)
On the Convergence of Alternating Steepest Descent Method for Solving Linear Systems in Tensor Format Representations
11:05 - 11:30
Martijn Boussé (Department of Electrical Engineering ESATSTADIUS KU Leuven)
Kronecker Product Equations and Applications
11:30 - 11:55
Giampaolo Mele (KTH Royal Institute of Technology)
The waveguide eigenvalue problem and the tensor infinite Arnoldi method
11:55 - 12:20
Venera Khoromskaia (Max-Planck Institute for Mathematics in the Sciences)
Assembled tensor method for summation of long range potentials on finite 3D lattices with defects
afternoon
14:45 - 15:10
Beatrice Meini (University of Pisa)
On the extension of Brauer's theorem to matrix polynomials with applications to quadratic matrix equations
15:10 - 15:35
Zvonimir Bujanovic (University of Zagreb)
A Low-Rank Quadratic ADI Algorithm for Algebraic Riccati Equations
15:35 - 16:00
Heiko K Weichelt (Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg)
Inexact Kleinman--Newton-ADI method including line search applied to large-scale algebraic Riccati equations
16:00 - 16:30
Coffee Break
16:30 - 16:55
Alvaro Barreras (Centro Universitario de la Defensa Spain)
SBD matrices and extension to tensors
16:55 - 17:20
Antoine Gautier (Department of Mathematics and Computer Science Saarland University Germany)
Perron-Frobenius Theorem and Power Method for the maximal $ell^{p_1,ldots,p_m}$ singular vectors of non-negative Tensors
17:20 - 17:45
Petar Sirkovic (EPF Lausanne)
A Reduced Basis approach to large-scale pseudospectra computation
17:45 - 18:10
Natasa Strabic (University of Manchester)
A framework for principal pivot transforms of quasidefinite matrices
Tuesday, September 22, 2015
morning
09:00 - 09:45
Bart Vandereycken (Université de Genéve, section of Mathematics, Geneve (CH))
Riemannian optimisation with rank contraints: preconditioning and rank adaptivity view abstract Bart Vandereycken
Riemannian optimisation with rank contraints: preconditioning and rank adaptivity
The minimisation of a smooth objective function subject to a matrix rank constraint can sometimes be very effectively solved by methods from Riemannian optimisation. This is for instance the case with the low-rank matrix completion problem or the solution of PDEs on square domains like the Lyapunov equation. However, the theory of Riemannian optimisation leaves some questions unanswered regarding the practical application of such algorithms. I will focus on two such questions. The first is how the metric has a significant impact on the convergence of the numerical methods. This is related to how Newton’s method can be seen as a variable metric in numerical optimisation and to general preconditioning techniques. The second topic is rank adaptivity. In rank-constrained optimisation, one does typically not know the rank a priori but may be searching for the smallest rank satisfying a certain criterion, like a small residual. I will explain how the geometry of the tangent cone of the variety of matrices of bounded rank can be incorporated so as to obtain rank adaptive algorithms that stay true to the manifold philosophy.
09:45 - 10:10
Jens Saak (Max Planck Institute for Dynamics of Complex Technical Systems)
Solving large-scale differential matrix equations
10:10 - 10:40
Coffee Break
10:40 - 11:05
Patrick Kuerschner (Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg)
Nearly optimal automatic shifts for the low-rank ADI iteration.
11:05 - 11:30
Bruno Iannazzo (Università di Perugia Italy)
A generalized $star$-Sylvester matrix equation.
11:30 - 11:55
Elias Jarlebring (KTH Royal institute of technology)
Iterative methods for the delay Lyapunov equation with T-Sylvester preconditioning
11:55 - 12:20
Javier Gonzalez (Departamento de Matematicas Universidad Carlos III de Madrid Spain)
Projection methods for large T-Sylvester equations
afternoon
14:45 - 15:10
Davide Palitta (Alma Mater Studiorum Università di Bologna)
Matrix-equation-based strategies for convection-diffusion equations.
15:10 - 15:35
Mattia Tani (Università di Pavia)
Methods for Sylvester equation in the isogeometrical solution of Laplace equation
15:35 - 16:00
Reinaldo Astudillo (Delft University of Technology)
Induced Dimension Reduction method for solving linear matrix equations
16:00 - 16:30
Coffee Break
16:30 - 16:55
Micol Ferranti (Dept Computer Science KU Leuven)
A twisted Hamiltonian QR algorithm
16:55 - 17:20
Suzana Miodragovi (Department of mathematics University of Osijek)
Relative Perturbation Theory for Definite Matrix Pairs and Hyperbolic Quadratic Eigenvalue Problem
17:20 - 17:45
Joab Winkler (The University of Sheffield United Kingdom)
Image Processing by Polynomial Computations
17:45 - 18:10
Alimohammad Nazari (Arak university of Iran)
Quasi Vandermonde matrices