Math Dept Logo, Info

Colloquium March 15

Date: Wednesday March 15

Time: 16:00 to 17:00

Place: 455 McBryde (Commons Room)

Speaker: Daniel Kressner of Univ of Zagreb

Title: Structured eigenvalue problems

Abstract

Matrix eigenvalue problems arise from practical applications usually only after a long process of simplifications, discretizations and linearizations. In most cases, the resulting matrices are highly structured. For example, matrix representations may contain redundancy, often in the form of sparsity, or inherit some physical properties from the original problem. Aimed at a wider audience, the purpose of this talk is to summarize some of the existing knowledge on the treatment of such eigenvalue problems.

Particular attention will be paid to the notion of structured condition numbers, which provide a first-order measure on the sensitivity of an eigenvalue or invariant subspace under perturbations that respect the matrix structure. A general framework covering Lie groups, Lie algebras and Jordan algebras associated with bilinear and sesquilinear forms is briefly presented. Also, it is shown that for many structures -- including Hamiltonian, symplectic, product and palindromic eigenvalue problems -- the Sylvester operator associated with an invariant subspace admits an orthogonal decomposition. This decomposition allows a simple derivation of structured condition numbers along with structure-preserving Newton methods.

This talk is based on joint work with Peter Benner, Ralph Byers, Heike Fassbender, Michael Karow and Francoise Tisseur.

Return to