On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations (Q2794610)
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scientific article; zbMATH DE number 6553831
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations |
scientific article; zbMATH DE number 6553831 |
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10 March 2016
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Hilbert space
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Landweber method
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Kaczmarz method
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systems of nonlinear ill-posed operator equations
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local tangential cone conditions
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convergence
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regularization
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numerical example
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large scale system
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On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations (English)
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This paper is about a new cyclic type of iteration methods for approximating solutions of systems of nonlinear ill-posed operator equations in Hilbert spaces. Based on the local tangential cone conditions, the authors establish convergence of the proposed methods within a regularization frame. The connection to the Landweber and Kaczmarz methods are discussed in detail. Both weak and strong convergence, exact data and randomized version of the methods are considered. Numerical examples are used to illustrate the superior performance of the proposed method for solving large scale systems of nonlinear ill-posed equations.
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