Convergence of a continuous analog of Newton's method for solving nonlinear equations

Authors

  • T. Zhanlav
  • O. Chuluunbaatar

Keywords:

iterative methods
rate of convergence
Newton-type methods
nonlinear equations

Abstract

The influence of the parameter in the continuous analog of Newton's method (CANM) on the convergence and on the convergence rate is studied. A τ-region of convergence of CANM for both scalar equations and equations in a Banach space is obtained. Some almost optimal choices of the parameter are proposed. It is also shown that the well-known higher order convergent iterative methods lead to the CANM with an almost optimal parameter. Several sufficient convergence conditions for these methods are obtained.

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Published

2009-12-05

Issue

Vol. 10 (2009): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biographies

T. Zhanlav

National University of Mongolia,
School of Engineering and Applied Sciences
University’s Street-3, Sukhbaatar District, 14201 Ulaanbaatar, Mongolia
• Academician

O. Chuluunbaatar

Joint Institute for Nuclear Research
• Senior Researcher

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