NDLI: Numerical and symbolic computation of the Lambert W function in $C^{nxn}$

Content Provider	ACM Digital Library
Author	Ding, Hui
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 $C^{nxn},$ 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 $C^{nxn}.$ 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 $C^{3x3},$ and implement solutions in the floating-point case, and the symbolic case, using Maple.
Starting Page	121
Ending Page	121
Page Count	1
File Format	PDF
ISSN	19322240
DOI	10.1145/1823931.1823957
Journal	ACM Communications in Computer Algebra (ACCA)
Volume Number	43
Issue Number	3/4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-02-05
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Computational Theory and Mathematics Computational Mathematics

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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