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Article
Empirical Versus Asymptotic Rate of Convergence of a Class of Methods for Solving a Polynomial Equation
Journal of Computational and Applied Mathematics (1997)
  • Tjalling Ypma, Western Washington University
  • Masao Igarashi
Abstract
Given alternative methods with identical order of convergence for solving the polynomial equation -(z) = 0, the method with the smaller asymptotic error constant might be assumed to be superior in terms of the number of iterations required for convergence. We present empirical evidence for a parameterized class of methods of second order showing that a parameter choice which does not correspond to the minimal asymptotic error constant may nevertheless be superior in practice.
Keywords
  • Polynomial equation,
  • Algebraic equation,
  • Asymptotic rate of convergence,
  • Newton-Raphson
Disciplines
Publication Date
September 15, 1997
Publisher Statement
Copyright © 1997 Published by Elsevier B.V. doi:10.1016/S0377-0427(97)00077-0
Citation Information
Tjalling Ypma and Masao Igarashi. "Empirical Versus Asymptotic Rate of Convergence of a Class of Methods for Solving a Polynomial Equation" Journal of Computational and Applied Mathematics Vol. 82 Iss. 1-2 Special Issue: 7th ICCAM 96 Congress (1997)
Available at: http://works.bepress.com/tjalling_ypma/17/