2007.90: The Solution of S exp(S) = A is Not Always the Lambert W Function of A
2007.90: Robert M. Corless, Hui Ding, Nicholas J. Higham and David J. Jeffrey (2007) The Solution of S exp(S) = A is Not Always the Lambert W Function of A. In: ISSAC '07: Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, July 29  August 01, 2007, Waterloo, Ontario, Canada.
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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 $y'(t) = A y(t1)$, which occur in some models of practical interest, especially in mathematical biology. This paper concentrates on the distinction between \emph{evaluating a matrix function} and \emph{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.
Item Type:  Conference or Workshop Item (Paper) 

Additional Information:  © ACM, (2007). This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 2007 international symposium on Symbolic and algebraic computation 2007, Waterloo, Ontario, Canada July 29  August 01, 2007. http://doi.acm.org/10.1145/1277548.1277565

Uncontrolled Keywords:  Matrix function; Lambert W function; nonlinear matrix equation 
Subjects:  MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis 
MIMS number:  2007.90 
Deposited By:  Nick Higham 
Deposited On:  17 August 2007 
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