Pade approximation for the exponential of a block triangular matrix

被引：40

作者：

Dieci, L ^{[1
]}

Papini, A

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Univ Florence, Dipartimento Energet S Stecco, I-50134 Florence, Italy

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 308卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

exponential; scaling and squaring; Pade approximation;

D O I：

10.1016/S0024-3795(00)00042-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we obtain improved error bounds for Pade approximations to e(A) when A is block triangular. As a result, improved scaling strategies ensue which avoid some common overscaling difficulties. (C) 2000 Elsevier Science Inc. All rights reserved.

引用

收藏

页码：183 / 202

页数：20

相关论文

共 15 条

[1] The Pade method for computing the matrix exponential [J].

Arioli, M ;

Codenotti, B ;

Fassino, C .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 240 (240) :111-130

[2] NUMERICAL-INTEGRATION OF ORDINARY DIFFERENTIAL-EQUATIONS ON MANIFOLDS [J].

CROUCH, PE ;

GROSSMAN, R .

JOURNAL OF NONLINEAR SCIENCE, 1993, 3 (01) :1-33

[3] Conditioning and Pade approximation of the logarithm of a matrix [J].

Dieci, L ;

Papini, A .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2000, 21 (03) :913-930

[4] PADE APPROXIMATIONS TO OPERATOR EXPONENTIAL [J].

FAIR, W ;

LUKE, YL .

NUMERISCHE MATHEMATIK, 1970, 14 (04) :379-&

[5]

Golub G. H., 2013, Matrix Computations

[6]

HAIRER E, 1991, SOLVING ORDINARY D 2

[7] PERTURBATION-THEORY AND BACKWARD ERROR FOR AX-XB=C [J].

HIGHAM, NJ .

BIT NUMERICAL MATHEMATICS, 1993, 33 (01) :124-136

[8] Exponential integrators for large systems of differential equations [J].

Hochbruck, M ;

Lubich, C ;

Selhofer, H .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 19 (05) :1552-1574

[9] On Krylov subspace approximations to the matrix exponential operator [J].

Hochbruck, M ;

Lubich, C .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) :1911-1925

[10]

Kagstrom B., 1977, BIT (Nordisk Tidskrift for Informationsbehandling), V17, P39, DOI 10.1007/BF01932398