The solution of s exp(s) = a is not always the lambert w function of a

Authors:
Robert M. Corless;Hui Ding;Nicholas J. Higham;David J. Jeffrey
Affiliations:
University of Western Ontario;University of Western Ontario;The University of Manchester, Manchester, UK;University of Western Ontario
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

Citing 3
Cited 2

Topics in matrix analysis

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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.