lambertwmatrix(k,A)

Computes the determination k of the Lambert W function of A

W=LAMBERTWMATRIX(k,A) computes the determination k of the Lambert W function of A
k: branch of the Lambert W function
A: matrix whose Lambert W is required
The algorithm is based on the Newton iteration with a heuristic stategy for the initial value based depending on the branch. The initial value is obtained truncating some series expansion of the Lambert W function around the branch points and infinity.

Reference:
M. Fasi, N. J. Higham and B. Iannazzo, An algorithm for the matrix Lambert W function, SIAM J. Matrix Anal. Appl., 36-2 (2015), pp. 669-685.