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We derive a priori residual-type bounds for the Arnoldi approximation of amatrix function and a strategy for setting the iteration accuracies in theinexact Arnoldi approximation of matrix functions. Such results are based onthe decay behavior of the entries of functions of banded matrices.Specifically, we will use a priori decay bounds for the entries of functions ofbanded non-Hermitian matrices by using Faber polynomial series. Numericalexperiments illustrate the quality of the results.

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