Solving systems of nonlinear equations In using a rotating hyperplane in

Abstract

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.

Keywords:

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

1980 Mathematics Subject Classification (1985 Revision):

• 65H10

C.R. Category:

• G.1.5