Abstract
This article describes an efficient and robust algorithm and implementation for the evaluation of the Wright ω function in IEEE double precision arithmetic over the complex plane.
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Software for Complex Double-Precision Evaluation of the Wright ω Function
- Corless, R. M. and Jeffrey, D. J. 1996. The unwinding number. SIGSAM BULLETIN: Comm. Comput. Algebra 30, 2:116, 28--35. Google ScholarDigital Library
- Corless, R. M. and Jeffrey, D. J. 2002. The Wright ? function. In Artificial Intelligence, Automated Reasoning, and Symbolic Computation, J. Calmet, B. Benhamou, O. Caprotti, L. Henocque, and V. Sorge Eds. Lecture Notes in Artificial Intelligence, vol. 2385, Springer, New York, 76--89. Google ScholarDigital Library
- Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., and Knuth, D. E. 1996. On the Lambert W function. Adv. Computat. Math. 5, 329--359.Google ScholarCross Ref
- Corless, R. M., Jeffrey, D. J., Watt, S. M., and Davenport, J. H. 2000. “According to Abramowitz and Stegun” or arccoth needn't be uncouth. ACM SIGSAM Bull. 34, 2, 58--65. Google ScholarDigital Library
- de Dinechin, F., Lauter, C., and Muller, J.-M. 2007. Fast and correctly rounded logarithms in doubleprecision. Theoret. Inf. Appl. 41, 1, 85--102.Google ScholarCross Ref
- Defour, D., Hanrot, G., Lefevre, V., Muller, J. M., Revol, N., and Zimmermann, P. 2004. Proposal for a standardization of mathematical function implementation in floating-point arithmetic. Numer. Algor. 37, 1, 367--375.Google ScholarCross Ref
- Ding, H. 2009. Numerical and symbolic computation of the Lambert W function in Cn×n. Ph.D. thesis, University of Western Ontario, Ontario, Canada. Google ScholarDigital Library
- Ezquerro, J. and Hernández, M. 2009. An optimization of Chebyshev's method. J. Complex. 25, 343--361. Google ScholarDigital Library
- Fritsch, F. N., Shafer, R. E., and Crowley, W. P. 1973. Solution of the transcendental equation wew = x. Comm. ACM 16, 2, 123--124. Google ScholarDigital Library
- Graham, R. L., Knuth, D. E., and Patashnik, O. 1994. Concrete Mathematics. Addison-Wesley, Boston, MA.Google Scholar
- Kung, H. T. and Traub, J. F. 1974. Optimal order of one-point and multipoint iteration. J. ACM 21, 4, 643--651. Google ScholarDigital Library
- Kung, H. T. and Traub, J. F. 1976. Optimal order and efficiency for iterations with two evaluations. SIAM J. Numer. Anal. 13, 1, 84--99.Google ScholarDigital Library
- Schröder, E. 1870. Ueber unendlich viele algorithmen zur auflösung der gleichungen. Math. Ann. 2, 2, 317--365.Google ScholarCross Ref
- Stewart, G. W. 1993. On infinitely many algorithms for solving equations. (Translation of paper by E. Schröder).Google Scholar
- Wright, E. M. 1959. Solution of the equation zez = a. Bull. Amer. Math Soc. 65, 89--93.Google ScholarCross Ref
Index Terms
- Algorithm 917: Complex Double-Precision Evaluation of the Wright ω Function
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