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.
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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:  MIMS Preprint 

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 PUBLICATION, {VOL#, ISS#, (DATE)} http://doi.acm.org/10.1145/nnnnnn.nnnnnn

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:  28 May 2007 
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 The Solution of S exp(S) = A is Not Always the Lambert W Function of A (deposited 17 August 2007)
 The Solution of S exp(S) = A is Not Always the Lambert W Function of A (deposited 28 May 2007) [Currently Displayed]
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