Abstract
Broyden's method is formulated for the solution of nonlinear operator equations in Hilbert spaces. The algorithm is proven to be well defined and a linear rate of convergence is shown. Under an additional assumption on the initial approximation for the derivative we prove the superlinear rate of convergence.
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Sachs, E.W. Broyden's method in Hilbert space. Mathematical Programming 35, 71–82 (1986). https://doi.org/10.1007/BF01589442
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DOI: https://doi.org/10.1007/BF01589442