A termination criterion for iterative methods used to find the zeros of polynomials

Author:
Masao Igarashi

Journal:
Math. Comp. **42** (1984), 165-171

MSC:
Primary 65H05; Secondary 65G99

DOI:
https://doi.org/10.1090/S0025-5718-1984-0725991-X

MathSciNet review:
725991

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Abstract | References | Similar Articles | Additional Information

Abstract: A new criterion for terminating iterations when searching for polynomial zeros is described. This method does not depend on the number of digits in the mantissa; moreover, it can be used to determine the accuracy of the resulting zeros. Examples are included.

**[1]**S. Yamashita & S. Satake, "On the calculation limit of roots of algebraic equations,"*Information Processing in Japan.*, v. 7, 1967, pp. 18-23. MR**0235724 (38:4027)****[2]**S. Hirano,*Numerical Solution of Algebraic Equations by Floating-Point Arithmetic*, Thesis, Nihon Univ., 1980.**[3]**G. Peter & J. H. Wilkinson, "Practical problems arising in the solution of polynomial equations,"*J. Inst. Math. Appl.*, v. 8, 1971, pp. 16-35. MR**0298931 (45:7980)****[4]**M. Igarashi, "Zeros of polynomials and an estimation of its accuracy,"*J. Inform. Process.*, v. 5, 1982, pp. 172-175. MR**686680 (84e:65045)****[5]**I. O. Kerner, "Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen,"*Numer. Math.*, v. 8, 1966, pp. 290-294. MR**0203931 (34:3778)****[6]**O. Aberth, "Iteration methods for finding all zeros of a polynomial simultaneously,"*Math. Comp.*, v. 27, 1973, pp. 339-344. MR**0329236 (48:7578)****[7]**B. T. Smith, "Error bounds for zeros of a polynomial based upon Gerschgorin's theorem,"*J. Assoc. Comput. Mach.*, v. 17, 1970, pp. 661-674. MR**0279998 (43:5719)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1984-0725991-X

Keywords:
Algebraic equation,
zeros of polynomials,
round-off errors

Article copyright:
© Copyright 1984
American Mathematical Society