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Convergence rate results for steepest descent type method for nonlinear ill-posed equations. (English) Zbl 1411.65078
Summary: Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper.

65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
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