Solving systems of nonlinear equations In using a rotating hyperplane in

A procedure which accelerates the convergence of iterative methods for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in is introduced. This procedure uses a rotating hyperplane in , whose rotation axis depends on the current approximation n-1 of components...

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Veröffentlicht in:International journal of computer mathematics 1990-01, Vol.35 (1-4), p.133-151
Hauptverfasser: Grapsa, T.N., Vrahatis, M.N., Bountis, T.C.
Format: Artikel
Sprache:eng
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Zusammenfassung:A procedure which accelerates the convergence of iterative methods for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in is introduced. This procedure uses a rotating hyperplane in , whose rotation axis depends on the current approximation n-1 of 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.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207169008803894