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

Published: 29 July 2007 Publication History

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.

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cover image ACM Conferences
ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation
July 2007
406 pages
ISBN:9781595937438
DOI:10.1145/1277548
  • General Chair:
  • Dongming Wang
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 29 July 2007

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Author Tags

  1. lambert w function
  2. matrix function
  3. nonlinear matrix equation

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ISSAC07
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ISSAC07: International Symposium on Symbolic and Algebraic Computation
July 29 - August 1, 2007
Ontario, Waterloo, Canada

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  • (2018)All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox–Wright function: illustration for genome multiplicity in survival of irradiated cellsJournal of Mathematical Chemistry10.1007/s10910-018-0985-357:1(59-106)Online publication date: 5-Dec-2018
  • (2017)Synthesis of the proportional integral controller for a non-minimum phase high order system by using the Lambert W function2017 13th International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS)10.1109/TELSKS.2017.8246319(439-442)Online publication date: Oct-2017
  • (2017)Synthesis of the proportional integral controller for a minimum phase high order system by using the lambert W function2017 IEEE 15th International Symposium on Intelligent Systems and Informatics (SISY)10.1109/SISY.2017.8080546(000169-000174)Online publication date: Sep-2017
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  • (2009)Pore pressure development beneath the décollement at the Nankai subduction zone: Implications for plate boundary fault strength and sediment dewateringJournal of Geophysical Research10.1029/2008JB006205114:B7Online publication date: 1-Jul-2009
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