A restarted Krylov subspace method for the evaluation of matrix functions

被引：93
|
作者：
Eiermann, Michael [1 ]
Ernst, Oliver G. [1 ]
机构：
[1] Tech Univ Bergakad, Inst Numer Math & Optimierung, D-09596 Freiburg, Germany
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2006年 / 44卷 / 06期
关键词：
matrix function; Krylov subspace approximation; Krylov projection method; restarted Krylov subspace method; linear system of equations; initial value problem;
D O I：
10.1137/050633846
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show how the Arnoldi algorithm for approximating a function of a matrix times a vector can be restarted in a manner analogous to restarted Krylov subspace methods for solving linear systems of equations. The resulting restarted algorithm reduces to other known algorithms for the reciprocal and the exponential functions. We further show that the restarted algorithm inherits the superlinear convergence property of its unrestarted counterpart for entire functions and present the results of numerical experiments.
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页码：2481 / 2504
页数：24
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