Title: Rational Krylov methods for the approximation of matrix functions

Speaker: Lothar Reichel

Affiliation: Kent State University

abstract:
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The need to evaluate expressions of the form $f(A)v$, where $A$ is a large
sparse or structured matrix, $v$ is a vector, and $f$ is a nonlinear
function, arises in many applications. The rational Krylov subspace method
can be an attractive scheme for computing approximations of such expressions.
This method projects the approximation problem onto a rational Krylov
subspace
of fairly small dimension, and then solves the small approximation problem
so obtained. We focus on the situation when $A$ is symmetric and the
rational functions have only one pole on the real axis. Then an orthogonal
basis for this subspace can be generated using short recursion formulas.
These
formulas are derived using properties of Laurent polynomials. The matrix of
the projected problem is pentadiagonal. We will discuss its structure and
present applications. The talk presents joint work with B. Beckermann and
C. Jagels.