PROJECTION-ITERATION REALIZATION OF A NEWTON-LIKE METHOD FOR SOLVING NONLINEAR OPERATOR EQUATIONS

Liudmyla L. Hart

Анотація

We consider the problem of existence and location of a solution of a nonlinear
operator equation with a Fr´echet differentiable operator in a Banach space and present the convergence results for a projection-iteration method based on a Newton-like method under the Cauchy’s conditions, which generalize the results for the projection-iteration realization of the Newton-Kantorovich method. The proposed method unlike the traditional interpretation is based on the idea of whatever approximation of the original equation by a sequence of approximate operator equations defined on subspaces of the basic space with the subsequent application of the Newton-like method to their approximate solution. We prove the convergence theorem, obtain the error estimate and discuss the advantages of the proposed approach and some of its modifications.

Ключові слова

nonlinear equation; Fr´echet differentiable operator; Newton-like method; projection-iteration method; approximation; convergence; error estimate

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Посилання

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DOI: http://dx.doi.org/10.15421/141903

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