期刊
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
卷 36, 期 2, 页码 669-685出版社
SIAM PUBLICATIONS
DOI: 10.1137/140997610
关键词
Lambert W function; primary matrix function; Newton method; matrix iteration; numerical stability; Schur-Parlett method
资金
- Collegio Superiore di Bologna
- European Research Council Advanced Grant MATFUN [267526]
- Engineering and Physical Sciences Research Council [EP/I01912X/1]
- Istituto Nazionale di Alta Matematica, INdAM-GNCS Project
- Engineering and Physical Sciences Research Council [EP/I01912X/1] Funding Source: researchfish
- EPSRC [EP/I01912X/1] Funding Source: UKRI
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.
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