A multistep iterative method for a nonlinear equation by using Durand-Kerner type auxiliary function

• SAKURAI Tetsuya

  Institute of Information Sciences and Electronics, University of Tsukuba

• SUGIURA Hiroshi

  Faculty of Engineering, Nagoya University

• TORII Tatsuo

  Faculty of Engineering, Nagoya University

Bibliographic Information

Other Title

• Durand-Kerner型補助関数を用いた非線形方程式の多段反復解法

Abstract

In this paper an iterative formula for the simultaneous determination of solutions of a nonlinear equation f(z)=0 is proposed. The Durand-Kerner method which is one of simultaneous iterative methods uses only function values of f(z) and does not require any higher order derivatives of f(z). Whereas it is applicable for only polynomial equations. Our method is based on the rational interpolation of f(z) on several points of approximation without derivatives of f(z) as the Durand-Kerner method. Moreover, it is applicable not only for polynomial equations but also for transcendental equations.

Journal

• Transactions of the Japan Society for Industrial and Applied Mathematics

  Transactions of the Japan Society for Industrial and Applied Mathematics 4 (2), 67-80, 1994

  The Japan Society for Industrial and Applied Mathematics

Details

• CRID: 1390282680745196032
• NII Article ID: 110001883571
• NII Book ID: AN10367166
• DOI: 10.11540/jsiamt.4.2_67
• ISSN: 24240982
• Text Lang: ja
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed