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BROYDEN'S METHOD FOR OPERATORS WITH REGULARLY CONTINUOUS DIVIDED DIFFERENCES

  • Galperin, Anatoly M.
  • Received : 2014.02.02
  • Published : 2015.01.01

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 assumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden's iterations. To demonstrate practical merits of Broyden's method, we use it for numerical solution of three nontrivial infinite-dimensional problems.

Keywords

nonlinear operator equations;Broyden's method;convergence analysis;regular continuity

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