Solving systems of nonlinear equations in rn using a rotating hyperplane in rn+1

T. N. Grapsa, M. N. Vrahatis, T. C. Bountis

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5 Citations (Scopus)

Abstract

A procedure which accelerates the convergence of iterative methods for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in Rn is introduced. This procedure uses a rotating hyperplane in Rn +1, whose rotation axis depends on the current approximation of n - 1 components of the solution. The proposed procedure is applied here on the traditional Newton's method and on a recently proposed “dimension-reducing” method [5] which incorporates the advantages of nonlinear SOR and Newton's algorithms. In this way, two new modified schemes for solving nonlinear systems are correspondingly obtained. For both of these schemes proofs of convergence are given and numerical applications are presented.

Original languageEnglish
Pages (from-to)133-151
Number of pages19
JournalInternational Journal of Computer Mathematics
Volume35
Issue number1-4
DOIs
Publication statusPublished - Jan 1990

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Keywords

  • Newton's method
  • bisection method
  • dimension-reducing method
  • implicit function theorem
  • imprecise function values
  • m-step SOR-Newton
  • nonlinear SOR
  • nonlinear equations
  • numerical solution
  • quadratic convergence
  • reduction to one-dimensional equations
  • zeros

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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