The Solution of S exp (S) = A is Not Always the Lambert W Function of A

被引：0

作者：

Corless, Robert M. ^{[1
]}

Ding, Hui ^{[1
]}

Higham, Nicholas J.

Jeffrey, David J. ^{[1
]}

机构：

[1] Univ Western Ontario, Ontario Res Ctr Comp Algebra, London, ON, Canada

来源：

ISSAC 2007: PROCEEDINGS OF THE 2007 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION | 2007年

关键词：

Matrix function; Lambert W function; nonlinear matrix equation;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the solutions of the matrix equation S exp(S) = A. Our motivation comes from the study of systems of delay differential equations y'(t) = Ay(t - 1), which occur in some models of practical interest, especially in mathematical biology. This paper concentrates on the distinction between evaluating a matrix function and solving a matrix equation. In particular, it shows that the matrix Lambert W function evaluated at the matrix A does not represent all possible solutions of S exp(S) = A. These results can easily be extended to more general matrix equations.

引用

页码：116 / 121

页数：6

共 14 条

[1] Bellman R., 1963, DIFFERENTIAL DIFFERE
[2] Approximating the logarithm of a matrix to specified accuracy
Cheng, SH
Higham, NJ
Kenney, CS
Laub, AJ
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2001, 22 (04) : 1112 - 1125
[3] Corless R. M., 2002, LECT NOTES COMPUT SC, V2385, P76, DOI DOI 10.1007/3-540-45470-510
[4] On the Lambert W function
Corless, RM
Gonnet, GH
Hare, DEG
Jeffrey, DJ
Knuth, DE
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 5 (04) : 329 - 359
[5] A Schur-Parlett algorithm for computing matrix functions
Davies, PI
Higham, NJ
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 25 (02) : 464 - 485
[6] Gantmacher F R, 1959, THEORY MATRICES, VI
[7] Heffernan JM., 2006, MATH SCI, V31, P21
[8] Stable iterations for the matrix square root
Higham, NJ
[J]. NUMERICAL ALGORITHMS, 1997, 15 (02) : 227 - 242
[9] HIGHAM NJ, 2006, HDB LINEAR ALGEBRA
[10] Horn R.A., 1991, TOPICS MATRIX ANAL

← 1 2 →