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The column-updating method for solving nonlinear equations in Hilbert space. (English) Zbl 0752.65047

Authors’ summary: The second author introduced the column-updating method for solving systems of nonlinear equations [Computing 33, 353-362 (1984; Zbl 0546.90102)]. In this paper we formulate this method for the solution of nonlinear operator equations in Hilbert spaces. We prove a local superlinear convergence result. We describe a new implementation for large-scale sparse finite dimensional problems and we present a numerical comparison of this implementation against C. G. Broyden’s method [Math. Comput. 19, 577–593 (1965; Zbl 0131.13905)] and L. K. Schubert’s method [ibid. 24, 27–30 (1970; Zbl 0198.49402)].

MSC:

65J15 Numerical solutions to equations with nonlinear operators
65H10 Numerical computation of solutions to systems of equations
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References:

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