Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices
This work provides theoretical guarantees and practical guidance for inexact Arnoldi methods, benefiting researchers and practitioners in numerical linear algebra and scientific computing.
The paper derives a priori residual-type bounds for the Arnoldi approximation of matrix functions and a strategy for setting iteration accuracies in inexact Arnoldi methods, based on decay properties of functions of banded non-Hermitian matrices. Numerical experiments demonstrate the quality of the results.
We derive a priori residual-type bounds for the Arnoldi approximation of a matrix function and 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, we will use a priori decay bounds for the entries of functions of banded non-Hermitian matrices by using Faber polynomial series. Numerical experiments illustrate the quality of the results.