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 proceedingConference 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 languageEnglish
    Title of host publicationProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC|Proc Int Symp Symbol Algebraic Comput ISSAC
    Pages116-121
    Number of pages5
    DOIs
    Publication statusPublished - 2007
    EventISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation - London, ON
    Duration: 1 Jul 2007 → …

    Conference

    ConferenceISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation
    CityLondon, ON
    Period1/07/07 → …

    Keywords

    • Lambert w function
    • Matrix function
    • Nonlinear matrix equation

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