Journal of the
Korean Mathematical Society JKMS

We present a new convergence analysis of popular Broyden's method in the Banach/Hilbert space setting which is applicable to nonsmooth 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

MSC numbers: 47J05, 47J25, 65J15