Using nonorthogonal Lanczos vectors in the computation of matrix functions

被引：57

作者：

Druskin, V

Greenbaum, A

Knizhnerman, L

机构：

[1] Schlumberger Doll Res Ctr, Ridgefield, CT 06877 USA

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[3] Cent Geophys Expedit, Moscow 123298, Russia

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 1998年 / 19卷 / 01期

关键词：

Lanczos algorithm; iterative methods; matrix exponential; finite precision arithmetic;

D O I：

10.1137/S1064827596303661

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Lanczos algorithm uses a three-term recurrence to construct an orthonormal basis for the Krylov space corresponding to a symmetric matrix A and a nonzero starting vector phi. The vectors and recurrence coefficients produced by this algorithm can be used for a number of purposes, including solving linear systems Au = phi and computing the matrix exponential e(-tA)phi. Although the vectors produced in finite precision arithmetic are not orthogonal, we show why they can still be used effectively for these purposes.

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收藏

页码：38 / 54

页数：17

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