Orthogonal polynomial expansions for the matrix exponential

被引：16

作者：

Moore, Gerald ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 03期

关键词：

Matrix exponential; Chebyshev polynomial; Legendre polynomial; Laguerre polynomial; SQUARING METHOD; COMPUTATION; ALGORITHM; RECURRENCE;

D O I：

10.1016/j.laa.2010.09.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Many different algorithms have been suggested for computing the matrix exponential. In this paper, we put forward the idea of expanding in either Chebyshev, Legendre or Laguerre orthogonal polynomials. In order for these expansions to converge quickly, we cluster the eigenvalues into diagonal blocks and accelerate using shifting and scaling. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：537 / 559

页数：23

共 37 条

[1] A NEW SCALING AND SQUARING ALGORITHM FOR THE MATRIX EXPONENTIAL [J].

Al-Mohy, Awad H. ;

Higham, Nicholas J. .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2009, 31 (03) :970-989

[2]

[Anonymous], FUNCTIONS MATRIX THE

[3]

[Anonymous], 1974, INTRO ASYMPTOTICS SP

[4]

[Anonymous], 2004, ORTHOGONAL POLYNOMIA, DOI DOI 10.1093/OSO/9780198506720.001.0001, Patent No. 220512815

[5]

[Anonymous], 1969, SPECIAL FUNCTIONS TH

[6]

[Anonymous], 1975, AM MATH SOC COLLOQ P

[7] ALGORITHM - SOLUTION OF MATRIX EQUATION AX+XB = C [J].

BARTELS, RH ;

STEWART, GW .

COMMUNICATIONS OF THE ACM, 1972, 15 (09) :820-&

[8] ALGORITHM FOR COMPUTING REDUCING SUBSPACES BY BLOCK DIAGONALIZATION [J].

BAVELY, CA ;

STEWART, GW .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (02) :359-367

[9]

Boyd JohnP, 2001, CHEBYSHEV FOURIER SP

[10] A Schur-Parlett algorithm for computing matrix functions [J].

Davies, PI ;

Higham, NJ .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 25 (02) :464-485

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