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A note on some improvements of the simultaneous methods for determination of polynomial zeros. (English) Zbl 0512.65041


MSC:

65H05 Numerical computation of solutions to single equations
26C10 Real polynomials: location of zeros
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)

Citations:

Zbl 0403.65013
Full Text: DOI

References:

[1] Aberth, O., Iteration methods for finding all zeros of a polynomial simultaneously, Math. Computation, 27, 339-344 (1973) · Zbl 0282.65037
[2] Alefeld, G.; Herzberger, J., On the convergence speed of some algorithms for the simultaneous approximation of polynomial roots, SIAM J. Numer. Anal., 2, 237-243 (1974) · Zbl 0282.65038
[3] Börsch-Supan, W., A posteriori error bounds for the zeros of polynomials, Numer. Math., 6, 380-398 (1963) · Zbl 0133.08401
[4] Dočev, K., A modified Newton method for the simultaneous approximation of all roots of the given algebraic equation, Fiz.-Mat. Spis Bulgar. Akad. Nauk, 5, 136-139 (1962), (in Bulgarian)
[5] Dočev, K.; Byrnev, P., Certain modifications of Newton’s method for the approximate solution of algebraic equations, Z. Vyčisl. Mat. i Fiz., 4, 915-920 (1964) · Zbl 0152.14601
[6] Ehrlich, L. W., A modified Newton method for polynomials, Comm. ACM, 10, 107-108 (1967) · Zbl 0148.39004
[7] Kerner, I. O., Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen, Numer. Math., 8, 290-294 (1966) · Zbl 0202.43605
[8] Nourein, A. W., An iteration formula for simultaneous determination of the zeroes of a polynomial, J. Comput. Appl. Math., 4, 251-254 (1975) · Zbl 0315.65029
[9] Nourein, A. W., An improvement on two iteration methods for simultaneous determination of the zeroes of a polynomial, Int. Comput. Math., 3, 241-252 (1977) · Zbl 0403.65013
[10] Ortega, J. M.; Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York · Zbl 0241.65046
[11] Weierstrass, K., Neuer Beweis des Satzes, dass jede Ganze Rationale Function einer Veräderlichen dargestellt werden kann als ein Product aus Linearen Functionen derselben Veränderlichen, Ges. Werke, Vol. 3, 251-269 (1903)
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