Name
Abstract | ||
|---|---|---|
The Lambert W function is a multivalued complex function, first named in the computer algebra system Maple. We present iterative schemes and strategies for the numerical evaluation of all branches of the scalar complex Lambert W function to hardware precision with high computational efficiency, and present a set of rules for the simplification of special symbolic arguments. We also extend the numerical and symbolic computations to the Lambert W function in Cnxn, for n 1. In order to achieve high precision and computational efficiency, we evaluate a series of high order and classical iterative methods and strategies for the evaluation of the scalar Lambert W function. We then construct optimal iterative schemes for the evaluation of the complex Lambert W function in the IEEE oating point model. The schemes consist of variations on Newton and Halley iterations together with initial estimates generated using a variety of series approximations. We also study several classes of exact simplifications for the Lambert W function for symbolic arguments and give rules for their application. Finally, we consider the solutions of the matrix equation S exp(S) = A, where S and A are n x n matrices. The solutions are expressed in terms of extensions of the scalar Lambert W function to Cnxn. The solutions of the matrix equations consist not only of the matrix functions W(A); other solutions also exist. We focus first on solving the matrix equation in C3x3, and implement solutions in the floating-point case, and the symbolic case, using Maple. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1145/1823931.1823957 | ACM Comm. Computer Algebra |
Keywords | DocType | Volume |
symbolic case,scalar Lambert W function,symbolic argument,symbolic computation,matrix equation,special symbolic argument,Lambert W function,complex Lambert W function,scalar complex Lambert W,matrix function,multivalued complex function | Journal | 43 |
Issue | Citations | PageRank |
3/4 | 0 | 0.34 |
References | Authors | |
0 | 1 | |