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The optimal algorithm to evaluate $ x\sp{n}$ using elementary multiplication methods

Author: D. P. McCarthy
Journal: Math. Comp. 31 (1977), 251-256
MSC: Primary 68A20
MathSciNet review: 0428791
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Abstract: The optimality of the binary algorithm to evaluate $ {x^n}$ is established where x is an integer or a completely dense polynomial modulo m, n is a positive integer, and the multiplications are done using a simple improvement on the naive algorithm.

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

  • [1] D. E. KNUTH, The Art of Computer Programming, Vol. 2, Addison-Wesley, Reading, Mass., 1969. MR 44 # 3531. MR 633878 (83i:68003)
  • [2] W. M. GENTLEMAN, "Optimal multiplication chains for computing a power of a symbolic polynomial," Math. Comp., v. 26, 1972, pp. 935-939. MR 47 # 2855. MR 0314303 (47:2855)

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Keywords: Symbolic algebraic manipulation, computational complexity, optimal multiplication chains
Article copyright: © Copyright 1977 American Mathematical Society

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