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On broyden's method for the regularization of nonlinear ill-posed problems1

 

作者: Barbara Kaltenbacher,  

 

期刊: Numerical Functional Analysis and Optimization  （Taylor Available online 1998）
卷期: Volume 19, issue 7-8  

页码: 807-833

 

ISSN:0163-0563

 

年代: 1998

 

DOI:10.1080/01630569808816860

 

出版商: Marcel Dekker, Inc.

 

关键词: Nonlinear ill-posed problems;iterative reguarization methods;Broyden's method;stopping rule;convergence rates;65J15;65J20;47H17;65R30

 

数据来源: Taylor

 

摘要:

This paper is concerned with nonlinear ill-posed operator equationsF(x) =yand their approximate solution by a quasi-Newton method, namely a regularized version of Broyden's method. Under an assumption on the nonlinearity ofF(which is shown to be fulfilled for several examples of inverse problems) and with an appropriate stopping rule, local convergence and convergence rates results are proven. The theoretical results are illustrated by numerical tests.

 

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