SOLVING SYSTEMS OF NONLINEAR EQUATIONS IN Rn USING A ROTATING HYPERPLANE IN Rn"
نویسنده
چکیده
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 Rnil, 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.
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