{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:30:11Z","timestamp":1750307411562,"version":"3.41.0"},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"3\/4","license":[{"start":{"date-parts":[[2010,6,24]],"date-time":"2010-06-24T00:00:00Z","timestamp":1277337600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2010,6,24]]},"abstract":"<jats:p>\n            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\n            <jats:sup>nxn<\/jats:sup>\n            , for n &gt; 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            <jats:italic>n x n<\/jats:italic>\n            matrices. The solutions are expressed in terms of extensions of the scalar Lambert W function to C\n            <jats:sup>nxn<\/jats:sup>\n            . 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\n            <jats:sup>3x3<\/jats:sup>\n            , and implement solutions in the floating-point case, and the symbolic case, using Maple.\n          <\/jats:p>","DOI":"10.1145\/1823931.1823957","type":"journal-article","created":{"date-parts":[[2010,6,29]],"date-time":"2010-06-29T13:02:22Z","timestamp":1277816542000},"page":"121-121","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical and symbolic computation of the Lambert W function in C\n            <sup>nxn<\/sup>"],"prefix":"10.1145","volume":"43","author":[{"given":"Hui","family":"Ding","sequence":"first","affiliation":[{"name":"University of Western Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,6,24]]},"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1823931.1823957","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1823931.1823957","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:39:33Z","timestamp":1750246773000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1823931.1823957"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,24]]},"references-count":0,"journal-issue":{"issue":"3\/4","published-print":{"date-parts":[[2010,6,24]]}},"alternative-id":["10.1145\/1823931.1823957"],"URL":"https:\/\/doi.org\/10.1145\/1823931.1823957","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2010,6,24]]},"assertion":[{"value":"2010-06-24","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}