Journal Article10.1080/10637199608915570
Parallel polynomial evaluation by decoupling algorithm
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TL;DR: Decoupling algorithm proposed by Kowalik and Kumar for solving bidiagonal systems is simplified and modified by showing that only two stages of three stage algorithm is satisfactory to be used to evaluate polynomials.
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Abstract: Horner's algorithm of evaluating a polynomial is studied and formulated as a matrix equation Ax = c, with a special bidiagonal A. Decoupling algorithm proposed by Kowalik and Kumar [5] for solving bidiagonal systems is simplified and modified by showing that only two stages of three stage algorithm is satisfactory to be used to evaluate polynomials. Some numerical results are presented and discussed. It has been seen that the results are comparable with those of Dorn's [1].
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Citations
Parallel Algorithms to Evaluate Orthogonal Polynomial Series
TL;DR: Four parallel algorithms for the evaluation of finite series of orthogonal polynomials based on the Forsythe and Clenshaw sequential algorithms are introduced.
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Modified Dorn's Algorithm with Improved Speed-Up
Ayse Kiper
- 18 Aug 1996
TL;DR: The extension and the generalisation of the approach followed in [5] for Dorn's method by reformulating as a set of independent matrix equations with special bidiagonal coefficient matrices leading to improvement in the speed-up of the algorithm.
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References
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L. Hyafil,Hsiang-Tsung Kung +1 more
TL;DR: The authors prove upper bounds on speed-ups achievable by parallel computers for a particular problem, the solution of first order linear recurrences for Cmmp and ILLIAC 4.
Generalizations of Horner's rule for polynomial evaluation
TL;DR: Two generalizations of Horner's rule, sometimes referred to as the nesting rule, which allow for parallel computation are presented here.
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•Dissertation
Analysis and design of parallel algorithms
Richard C. Dunbar
- 01 Jan 1978
TL;DR: With the actual physical size of components being very small and the high circuit density, there is little scope for improving computation speech significantly by such means as even denser circuitry or still faster electronic components.
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