A family of preconditioned iteratively regularized methods for nonlinear minimization

Smirnova, Alexandra; Renaut, Rosemary A.

doi:10.1515/jiip.2009.027

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A Priori and A Posteriori Stopping Rules1

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2012

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“…The qualification order of this algorithm is M. When M = 1, one obtains (2.2) as a particular case. For G = L * L with L being a bounded linear operator and a less general source condition (2.1), the convergence analysis of the above scheme (as well as other Gauss-Newton-type methods with a linear penalty term L * L) has been conducted in [SR09].…”

Section: A Priori and A Posteriori Stopping Rulesmentioning

confidence: 99%

On convergence rates for iteratively regularized procedures with linear penalty terms

Smirnova¹

2012

Inverse Problems

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The impact of this paper is twofold. First, we study convergence rates of the iteratively regularized Gauss-Newton (IRGN) algorithm with a linear penalty term under a generalized source assumption and show how the regularizing properties of new iterations depend on the solution smoothness. Secondly, we introduce an adaptive IRGN procedure, which is investigated under a relaxed smoothness condition. The introduction and analysis of a more general penalty term are of great importance since, apart from bringing stability to the numerical scheme designed for solving a large class of applied inverse problems, it allows us to incorporate various types of a priori information available on the model. Both a priori and a posteriori stopping rules are investigated. For the a priori stopping rule, optimal convergence rates are derived. A numerical example illustrating convergence rates is considered.

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Section: A Priori and A Posteriori Stopping Rulesmentioning

confidence: 99%

On convergence rates for iteratively regularized procedures with linear penalty terms

Smirnova¹

2012

Inverse Problems

View full text Add to dashboard Cite

show abstract

A family of preconditioned iteratively regularized methods for nonlinear minimization

Cited by 1 publication

References 13 publications

On convergence rates for iteratively regularized procedures with linear penalty terms

On convergence rates for iteratively regularized procedures with linear penalty terms

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