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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Efficient multiple-precision evaluation of elementary functions
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by David M. Smith PDF
Math. Comp. 52 (1989), 131-134 Request permission

Abstract:

Let $M(t)$ denote the time required to multiply two t-digit numbers using base b arithmetic. Methods are presented for computing the elementary functions in $O({t^{1/3}}M(t))$ time.
References
  • Richard P. Brent, Multiple-precision zero-finding methods and the complexity of elementary function evaluation, Analytic computational complexity (Proc. Sympos., Carnegie-Mellon Univ., Pittsburgh, Pa., 1975) Academic Press, New York, 1976, pp. 151–176. MR 0423869
  • Richard P. Brent, Fast multiple-precision evaluation of elementary functions, J. Assoc. Comput. Mach. 23 (1976), no. 2, 242–251. MR 395314, DOI 10.1145/321941.321944
  • R. P. Brent, "A Fortran multiple-precision arithmetic package," ACM Trans. Math. Software, v. 4, 1978, pp. 57-70.
  • Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
  • Michael S. Paterson and Larry J. Stockmeyer, On the number of nonscalar multiplications necessary to evaluate polynomials, SIAM J. Comput. 2 (1973), 60–66. MR 314238, DOI 10.1137/0202007
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 52 (1989), 131-134
  • MSC: Primary 65D15; Secondary 26-04
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0971406-0
  • MathSciNet review: 971406