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Optimal algorithms for parallel polynomial evaluation. (English) Zbl 0256.68013


MSC:

68W99 Algorithms in computer science
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[1] Estrin, G., Organization of Computer System—The Fixed Plus Variable Structure Computer, (Proceedings Western Joint Computer Conference (May, 1960), AFIPS Press: AFIPS Press Montvale, NJ), 33-40
[2] Dorn, W. S., (Generalizations of Horner’s Rule for Polynomial Evaluation, Vol. 6 (1962), IBM J. Res. Dev.), 239-245 · Zbl 0128.37202
[3] Muraoka, Y., Parallelism Exposure and Exploitation in Programs, (Report No. 424 (1971), Department of Computer Science, University of Illinois: Department of Computer Science, University of Illinois Urbana-Champaign, IL)
[4] Knuth, D. E., (The Art of Computer Programming: II. Seminumerical Algorithms (1969), Addison-Wesley: Addison-Wesley Reading, MA), 422-444
[5] Winograd, S., On the Number of Multiplications Required to Compute Certain Functions, Proc. Nat. Acad. Sci. U.S.A., 58, 1840-1842 (1967) · Zbl 0189.47902
[6] Borodin, A., Horner’s Rule is Uniquely Optimal, (Kohavi, Z.; Paz, A., Proceedings International Symposium on the Theory of Machines and Computation. Proceedings International Symposium on the Theory of Machines and Computation, Haifa (August, 1971), Academic Press: Academic Press NY), 45-48
[7] Maruyama, K., Parallel Methods and Bounds of Evaluating Polynomials, (Report No. 427 (1971), Department of Computer Science, University of Illinois: Department of Computer Science, University of Illinois Urbana-Champaign, IL)
[8] Motzkin, T. S., Evaluation of Polynomials and Evaluation of Rational Functions, Bull. Amer. Math. Soc., 61, 163 (1955)
[9] Belaga, E. G., On Computing Polynomials in One Variable with Initial Conditioning of the Coefficients, Problemy Kibernet., 5, 7-15 (1961) · Zbl 0136.12605
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