BROYDEN’S METHOD FOR OPERATORS WITH REGULARLY CONTINUOUS DIVIDED DIFFERENCES
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We present a new convergence analysis of popular Broyden’s method in the Banach/Hilbert space setting which is applicable to non- smooth operators. Moreover, we do not assume a priori solvability of the equation under consideration. Nevertheless, without these simplifying as- sumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden’s iterations. To demonstrate practi- cal merits of Broyden’s method, we use it for numerical solution of three nontrivial infinite-dimensional problems.
Abstract
We present a new convergence analysis of popular Broyden’s method in the Banach/Hilbert space setting which is applicable to non- smooth operators. Moreover, we do not assume a priori solvability of the equation under consideration. Nevertheless, without these simplifying as- sumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden’s iterations. To demonstrate practi- cal merits of Broyden’s method, we use it for numerical solution of three nontrivial infinite-dimensional problems.
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