Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices

Abstract

This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix function together with a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay behavior of the entries of functions of banded matrices.

Specifically, a priori decay bounds for the entries of functions of banded non-Hermitian matrices will be exploited, using Faber polynomial approximation. Numerical experiments illustrate the quality of the results.

Keywords

• Arnoldi algorithm
• Inexact Arnoldi algorithm
• Matrix functions
• Faber polynomials
• Decay bounds
• Banded matrices