Publication
Journal of Computer and System Sciences
Paper

Evaluation of polynomials with super-preconditioning

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Abstract

Certain questions concerning the arithmetic complexity of univariate polynomial evaluation are considered. The principal technical results show that there exist polynomials f,g, and h with h = fg, such that h requires substantially fewer arithmetic operations than either f or g. However, if the coefficients of f are algebraically independent, then any h = fg is as hard to evaluate as f. The question of the relative complexities of f and fg is viewed as a special case of the following question: given an operator Δ which maps polynomials to sets of polynomials, what savings in arithmetic operations is achievable by evaluating some polynomial h ε{lunate} Δ(f) rather than f? Observations and open questions concerning several operators are discussed. © 1978.

Date

01 Jan 1978

Publication

Journal of Computer and System Sciences

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