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Frozen Landweber iteration for nonlinear ill-posed problems. (English) Zbl 1182.65085
Summary: We propose a modification of the Landweber iteration termed frozen Landweber iteration for nonlinear ill-posed problems. A convergence analysis for this iteration is presented. The numerical performance of this frozen Landweber iteration for a nonlinear Hammerstein integral equation is compared with that of the Landweber iteration. We obtain a shorter running time of the frozen Landweber iteration based on the same convergence accuracy.

65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47J06 Nonlinear ill-posed problems
45G10 Other nonlinear integral equations
65R20 Numerical methods for integral equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Full Text: DOI
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