A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions

Heinz Engl; Otmar Scherzer

doi:10.1088/0266-5611/14/5/002

A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions

Heinz Engl, Otmar Scherzer

Industrial Mathematics Institute

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

Abstract

In this paper, we present a new approach to a convergence theory for iterative methods for solving nonlinear ill-posed problems based on invariance conditions. It is applied to (modified) Landweber's method, Levenberg Marquardt, and Iteratively Regularized Gauß-Newton method.

Original language	English
Pages (from-to)	1081-1106
Number of pages	26
Journal	Inverse Problems
Volume	14
Issue number	5
DOIs	https://doi.org/10.1088/0266-5611/14/5/002
Publication status	Published - 1998

Fields of science

101 Mathematics
101020 Technical mathematics

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10.1088/0266-5611/14/5/002

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abstract = "In this paper, we present a new approach to a convergence theory for iterative methods for solving nonlinear ill-posed problems based on invariance conditions. It is applied to (modified) Landweber's method, Levenberg Marquardt, and Iteratively Regularized Gau{\ss}-Newton method.",

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AB - In this paper, we present a new approach to a convergence theory for iterative methods for solving nonlinear ill-posed problems based on invariance conditions. It is applied to (modified) Landweber's method, Levenberg Marquardt, and Iteratively Regularized Gauß-Newton method.

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U2 - 10.1088/0266-5611/14/5/002

DO - 10.1088/0266-5611/14/5/002

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JO - Inverse Problems

JF - Inverse Problems

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A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions

Abstract

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