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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Optimal multiplication chains for computing a power of a symbolic polynomial


Author: W. Morven Gentleman
Journal: Math. Comp. 26 (1972), 935-939
MSC: Primary 68A15
MathSciNet review: 0314303
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper shows that in a certain model of symbolic manipulation of algebraic formulae, the simple method of computing a power of a symbolic polynomial by repeated multiplication by the original polynomial is, in essence, the optimal method.


References [Enhancements On Off] (What's this?)

  • [1] W. M. Gentleman & G. Sande, ``Fast Fourier transforms--for fun and profit,'' Proceedings of the 1966 Fall Joint Computer Conference, AFIPS, Spartan Books, Washington, 1966, pp. 563-578.
  • [2] Donald E. Knuth, The art of computer programming, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Volume 1: Fundamental algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR 0378456 (51 #14624)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0314303-3
PII: S 0025-5718(1972)0314303-3
Keywords: Symbolic algebraic manipulation, optimal multiplication chains, complexity
Article copyright: © Copyright 1972 American Mathematical Society