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• W2109392496 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." @default.
• W2109392496 created "2016-06-24" @default.
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• W2109392496 date "2015-01-01" @default.
• W2109392496 modified "2023-09-23" @default.
• W2109392496 title "An Algorithm for the Matrix Lambert $W$ Function" @default.
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• W2109392496 doi "https://doi.org/10.1137/140997610" @default.
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