New England Numerical Analysis Day 2009

University of Rhode Island
Department of Mathematics, Lippitt Hall
April 4, 2009, 9:00am-5:30pm
main conference page

Error estimation and evaluation of matrix functions

Lothar Reichel, Kent State University

(joint work with B. Beckermann and C. Jagels)

The need to evaluate expressions of the form $f(A)$ or $f(A)b$, where $f$ is a nonlinear function, $A$ is a large sparse matrix, and $b$ is a vector, arises in many applications. We discuss how the Faber transform applied to the field of values of $A$ can be used to determine error bounds for popular polynomial and rational approximation methods based on the Arnoldi rational Arnoldi processes. The situation when $A$ is symmetric and the rational function has a preselected pole receives particular attention. In this case orthogonal bases of rational Krylov subspaces can be determined with short recursion relations. The talk presents joint work with B. Beckermann and C. Jagels.



Organizers

Jim Baglama (URI), Tom Bella (URI), Li Wu (URI).

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