On computational efficiency of the iterative methods for the simultaneous approximation of polynomial zeros

Gradimir V. Milovanović, Miodrag S. Petković

Type: Article

Publication Date: 1986-12-01

Citations: 28

DOI: https://doi.org/10.1145/22721.8932

Abstract

A measure of efficiency of simultaneous methods for determination of polynomial zeros, defined by the coefficient of efficiency, is considered. This coefficient takes into consideration (1) the R-order of convergence in the sense of the definition introduced by Ortega and Rheinboldt (Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, 1970) and (2) the number of basic arithmetic operations per iteration, taken with certain weights depending on a processor time. The introduced definition of computational efficiency was used for comparison of the simultaneous methods with various structures.

Locations

ACM Transactions on Mathematical Software - View - PDF

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+	Zur iterativen Auflösung algebraischer Gleichungen	1954	Hans J. Maehly
+	Solution of Equations and Systems of Equations	1967	E. I. Alexander Ostrowski
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+	Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation	1970	Wolfgang Börsch‐Supan
+ PDF Chat	Iteration methods for finding all zeros of a polynomial simultaneously	1973	Oliver Aberth
+	Iterative Methods for the Solution of Equations.	1967	David M. Young J. F. Traub
+	A note on some improvements of the simultaneous methods for determination of polynomial zeros	1983	Miodrag S. Petković Gradimir V. Milovanović
+	An improvement on Nourein's method for the simultaneous determination of the zeroes of a polynomial (An algorithm)	1977	A.W. Nourein
+	A posteriori error bounds for the zeros of polynomials	1963	W. B�rsch-Supan
+	On the Convergence Speed of Some Algorithms for the Simultaneous Approximation of Polynomial Roots	1974	Götz Alefeld Jürgen Herzberger