Numerical Linear and Multilinear Algebra
We study numerical methods for linear and nonlinear eigenvalue problems. This includes the development and analysis of new algorithms, (backward) error analysis, and the derivation of the associated (relative) perturbation theory. Special attention is given to linear, generalized, and polynomial eigenproblems with spectral symmetries. Special cases include:
- linear eigenproblems for Hamiltonian and symplectic matrices,
- generalized eigenproblems for skew-Hamiltonian/Hamiltonian, even, and positive definite matrix pencils,
- as well as even, gyroscopic, and hyperbolic polynomial eigenvalue problems.
Moreover, we investigate the solution of special linear systems of equations arising in PDE control and model reduction algorithms. This includes in particular
- recycling techniques for Krylov subspace solvers for systems with multiple-right hand sides and constant (or slowly varying) coefficient matrices,
- preconditioning techniqes for saddle point problems, and
- using tensor techniques to solve high-dimensional problems like stochastic Galerkin systems.