AN ALGORITHM FOR THE MATRIX LAMBERT W FUNCTION

作者：Fasi Massimiliano^*; Higham Nicholas J; Iannazzo Bruno

来源：SIAM Journal on Matrix Analysis and Applications, 2015, 36(2): 669-685.

DOI：10.1137/140997610

• Lambert W function
• primary matrix function
• Newton method
• matrix iteration
• numerical stability
• Schur-Parlett method

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.

• 出版日期2015
• 单位Perugia