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

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

Research output: Contribution to journalArticle

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 - 1990
Externally publishedYes

Fingerprint

System of Nonlinear Equations
Newton-Raphson method
Iterative methods
Nonlinear equations
Hyperplane
Nonlinear systems
Rotating
Transcendental
Newton Methods
Accelerate
Nonlinear Systems
Numerical Solution
Iteration
Approximation

Keywords

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

ASJC Scopus subject areas

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

Cite this

Solving systems of nonlinear equations in rn using a rotating hyperplane in rn+1. / Grapsa, T. N.; Vrahatis, M. N.; Bountis, T. C.

In: International Journal of Computer Mathematics, Vol. 35, No. 1-4, 1990, p. 133-151.

Research output: Contribution to journalArticle

Grapsa, T. N. ; Vrahatis, M. N. ; Bountis, T. C. / Solving systems of nonlinear equations in rn using a rotating hyperplane in rn+1. In: International Journal of Computer Mathematics. 1990 ; Vol. 35, No. 1-4. pp. 133-151.
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