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.
- Gentleman, W. M. and Sande, G. "Fast Fourier Transforms -- For Fun and Profit". Proceedings of the 1966 Fall Joint Computer Conference, AFIPS, Spartan Books, Washington (1966), pp. 563--578.Google Scholar
- Knuth, D. "The Art of Computer Programming: Volume II, Seminumerical Algorithms", Addison Wesley, Reading, Massachusetts (1968). Google ScholarDigital Library
Index Terms
- Optimal multiplication chains for computing a power of a symbolic polynomial
Recommendations
Certain classes of polynomial expansions and multiplication formulas
The authors first present a class of expansions in a series of Bernoulli polyomials and then show how this general result can be applied to yield various (known or new) polynomial expansions. The corresponding expansion problem involving the Euler ...
Computing polynomial resultants: Bezout's determinant vs. Collins' reduced P.R.S. algorithm
Algorithms for computing the resultant of two polynomials in several variables, a key repetitive step of computation in solving systems of polynomial equations by elimination, are studied. Determining the best algorithm for computer implementation ...
Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains
Let a,b and h be positive integers and S={x"1,...,x"h} be a set of h distinct positive integers. The hxh matrix (S^a)=((x"i,x"j)^a), having the ath power (x"i,x"j)^a of the greatest common divisor of x"i and x"j as its (i,j)-entry, is called the ath ...
Comments