期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 47, 期 5, 页码 3849-3883出版社
SIAM PUBLICATIONS
DOI: 10.1137/080741744
关键词
matrix function; polynomial approximation; rational approximation; Arnoldi process; rational Arnoldi process; error bound
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 n x n matrix, and b is an n-vector, arises in many applications. This paper describes how the Faber transform applied to the field of values of Lambda can be used to determine improved error bounds for popular polynomial approximation methods based on the Arnoldi process. Applications of the Faber transform to rational approximation methods and, in particular, to the rational Arnoldi process also are discussed.
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