A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems

Otmar Scherzer

doi:10.1080/01630569608816691

A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems

Otmar Scherzer

Industrial Mathematics Institute

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove that the steepest descent iteration and a two-step are stable methods for solving nonlinear ill-posed problems. For perturbed data with noise level delta we propose stopping rules that yield convergence of the iterates.

Original language	English
Pages (from-to)	197-214
Number of pages	18
Journal	Numerical Functional Analysis and Optimization
Volume	17
Issue number	1-2
DOIs	https://doi.org/10.1080/01630569608816691
Publication status	Published - 1996

Fields of science

101 Mathematics
101020 Technical mathematics

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10.1080/01630569608816691

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abstract = "In this paper we prove that the steepest descent iteration and a two-step are stable methods for solving nonlinear ill-posed problems. For perturbed data with noise level delta we propose stopping rules that yield convergence of the iterates.",

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DO - 10.1080/01630569608816691

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JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

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A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems

Abstract

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