A family of preconditioned iteratively regularized methods for nonlinear minimization

A. Smirnova; Rosemary Renaut

doi:10.1515/JIIP.2009.027

A family of preconditioned iteratively regularized methods for nonlinear minimization

A. Smirnova, Rosemary Renaut

Mathematical and Statistical Sciences, School of (SoMSS)

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

2 Scopus citations

Abstract

The preconditioned iteratively regularized Gauss-Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes M-times iterated Tikhonov regularization with line search. Numerical schemes illustrating the theoretical results are also presented.

Original language	English (US)
Pages (from-to)	405-418
Number of pages	14
Journal	Journal of Inverse and Ill-Posed Problems
Volume	17
Issue number	4
DOIs	https://doi.org/10.1515/JIIP.2009.027
State	Published - Jun 2009

Keywords

Gauss-Newton method
Ill-posed problem
Regularization
Stopping rule

ASJC Scopus subject areas

Applied Mathematics

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10.1515/JIIP.2009.027

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title = "A family of preconditioned iteratively regularized methods for nonlinear minimization",

abstract = "The preconditioned iteratively regularized Gauss-Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes M-times iterated Tikhonov regularization with line search. Numerical schemes illustrating the theoretical results are also presented.",

keywords = "Gauss-Newton method, Ill-posed problem, Regularization, Stopping rule",

author = "A. Smirnova and Rosemary Renaut",

note = "Funding Information: Second author: Supported by NSF grants DMS 0513214 and DMS 0652833",

year = "2009",

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AU - Smirnova, A.

AU - Renaut, Rosemary

N1 - Funding Information: Second author: Supported by NSF grants DMS 0513214 and DMS 0652833

PY - 2009/6

Y1 - 2009/6

N2 - The preconditioned iteratively regularized Gauss-Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes M-times iterated Tikhonov regularization with line search. Numerical schemes illustrating the theoretical results are also presented.

AB - The preconditioned iteratively regularized Gauss-Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes M-times iterated Tikhonov regularization with line search. Numerical schemes illustrating the theoretical results are also presented.

KW - Gauss-Newton method

KW - Ill-posed problem

KW - Regularization

KW - Stopping rule

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JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

IS - 4

ER -

A family of preconditioned iteratively regularized methods for nonlinear minimization

Abstract

Keywords

ASJC Scopus subject areas

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