The solution of S exp(S) = a is not always the lambert W function of A

Robert M. Corless; Hui Ding; David J. Jeffrey; Nicholas J. Higham

doi:10.1145/1277548.1277565

The solution of S exp(S) = a is not always the lambert W function of A

Robert M. Corless, Hui Ding, David J. Jeffrey, Nicholas J. Higham

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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. Copyright 2007 ACM.

Original language	English
Title of host publication	Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC\|Proc Int Symp Symbol Algebraic Comput ISSAC
Pages	116-121
Number of pages	5
DOIs	https://doi.org/10.1145/1277548.1277565
Publication status	Published - 2007
Event	ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation - London, ON Duration: 1 Jul 2007 → …

Conference

Conference	ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation
City	London, ON
Period	1/07/07 → …

Keywords

Lambert w function
Matrix function
Nonlinear matrix equation

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10.1145/1277548.1277565

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@inproceedings{c8a006667c3e4523a56007e82cd24760,

title = "The solution of S exp(S) = a is not always the lambert W function of A",

abstract = "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. Copyright 2007 ACM.",

keywords = "Lambert w function, Matrix function, Nonlinear matrix equation",

author = "Corless, {Robert M.} and Hui Ding and Jeffrey, {David J.} and Higham, {Nicholas J.}",

year = "2007",

doi = "10.1145/1277548.1277565",

language = "English",

isbn = "1595937439",

pages = "116--121",

booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC|Proc Int Symp Symbol Algebraic Comput ISSAC",

note = "ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation ; Conference date: 01-07-2007",

}

Corless, RM, Ding, H, Jeffrey, DJ & Higham, NJ 2007, The solution of S exp(S) = a is not always the lambert W function of A. in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC|Proc Int Symp Symbol Algebraic Comput ISSAC. pp. 116-121, ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation, London, ON, 1/07/07. https://doi.org/10.1145/1277548.1277565

TY - GEN

T1 - The solution of S exp(S) = a is not always the lambert W function of A

AU - Corless, Robert M.

AU - Ding, Hui

AU - Jeffrey, David J.

AU - Higham, Nicholas J.

PY - 2007

Y1 - 2007

N2 - 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. Copyright 2007 ACM.

AB - 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. Copyright 2007 ACM.

KW - Lambert w function

KW - Matrix function

KW - Nonlinear matrix equation

U2 - 10.1145/1277548.1277565

DO - 10.1145/1277548.1277565

M3 - Conference contribution

SN - 1595937439

SN - 9781595937438

SP - 116

EP - 121

BT - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC|Proc Int Symp Symbol Algebraic Comput ISSAC

T2 - ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation

Y2 - 1 July 2007

ER -

The solution of S exp(S) = a is not always the lambert W function of A

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