Fasi, Massimiliano and Higham, Nicholas J. and Iannazzo, Bruno (2015) An Algorithm for the Matrix Lambert W Function. SIAM Journal on Matrix Analysis and Applications, 36 (2). pp. 669685. ISSN 10957162
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Abstract
An algorithm is proposed for computing primary matrix Lambert $W$ functions of a square matrix $A$, which are solutions of the matrix equation $We^W = A$. The algorithm employs the Schur decomposition and blocks the triangular form in such a way that Newton's method can be used on each diagonal block, with a starting matrix depending on the block. A natural simplification of Newton's method for the Lambert $W$ function is shown to be numerically unstable. By reorganizing the iteration a new Newton variant is constructed that is proved to be numerically stable. Numerical experiments demonstrate that the algorithm is able to compute the branches of the matrix Lambert $W$ function in a numerically reliable way.
Item Type:  Article 

Uncontrolled Keywords:  Lambert $W$ function, primary matrix function, Newton method, matrix iteration, numerical stability, SchurParlett method 
Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis 
Depositing User:  Nick Higham 
Date Deposited:  12 Jul 2015 
Last Modified:  20 Oct 2017 14:13 
URI:  https://eprints.maths.manchester.ac.uk/id/eprint/2344 
Available Versions of this Item

An Algorithm for the Matrix Lambert W Function. (deposited 26 Nov 2014)

An Algorithm for the Matrix Lambert W Function. (deposited 07 Apr 2015)
 An Algorithm for the Matrix Lambert W Function. (deposited 12 Jul 2015) [Currently Displayed]

An Algorithm for the Matrix Lambert W Function. (deposited 07 Apr 2015)
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