An Algorithm for the Matrix Lambert $W$ Function

DOI10.1137/140997610zbMath1317.65116OpenAlexW2109392496WikidataQ56998635 ScholiaQ56998635MaRDI QIDQ5256534

Massimiliano Fasi, Nicholas J. Higham, Bruno Iannazzo

Publication date: 18 June 2015

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/140997610

zbMATH Keywords

algorithmnumerical stabilityNewton methodnumerical experimentmatrix equationmatrix iterationLambert \(W\) functionprimary matrix functionSchur-Parlett method

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Iterative numerical methods for linear systems (65F10) Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

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Uses Software

• mctoolbox
• DLMF
• Algorithm 432

Cites Work

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• Do the chain rules for matrix functions hold without commutativity?
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• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Functions of Matrices
• Exponential of a matrix, a nonlinear problem, and quantum gates