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Improving a method of search for solving polynomial equations. (English) Zbl 0877.65028
Summary: This paper is related to the Lehmer-Schur methods in numerical mathematics in the complex plane. It is shown that by a slight modification of the “optimized” Lehmer-Schur method of A. Galántai [Alkalmazott Mat. Lapok 11, 319-334 (1985; Zbl 0615.65070)], the “speed” quotient 0.6094 can be reduced to 0.5758. The crucial idea is based on a discrete geometrical observation.

MSC:
65H05 Numerical computation of solutions to single equations
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
12Y05 Computational aspects of field theory and polynomials (MSC2010)
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References:
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[2] Lehmer, D.H., Search procedures for polynomial equation solving, () · Zbl 0182.21503
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[6] Galántai, A., On the optimization of the Lehmer-Schur method [hungarian; English summary], Alk. mat. lapok [hungary], 11, 319-334, (1985) · Zbl 0615.65070
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