Theoretical and Numerical Study of Iteratively Truncated Newton’s Algorithm

Bakushinsky, A. B.; Smirnova, Alexandra; Liu, Hui

doi:10.1007/978-1-4614-7816-4_1

Applied Inverse Problems

2013

DOI: 10.1007/978-1-4614-7816-4_1

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Theoretical and Numerical Study of Iteratively Truncated Newton’s Algorithm

A. B. Bakushinsky

Alexandra Smirnova

Hui Liu

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2017

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Cited by 1 publication

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On TSVD regularization for a Broyden-type algorithm

Smirnova

2017

Journal of Inverse and Ill-Posed Problems

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An applied inverse problem in the form of a nonlinear operator equation on a pair of two Hilbert spaces is considered. In the lack of stability, a version of Broyden’s method regularized by truncated singular value decomposition (TSVD) is proposed in order to suppress the potential noise propagation and to reduce the cost associated with storage and inversion of the Fréchet derivative operator. An attractive feature of this study is that it does not rely on any restrictions on the nonlinearity of the operator and/or on the spectrum of the Fréchet derivative. For the numerical analysis of the proposed algorithm, a parameter identification problem in epidemiology is investigated.

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On TSVD regularization for a Broyden-type algorithm

Smirnova

2017

Journal of Inverse and Ill-Posed Problems

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show abstract

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Theoretical and Numerical Study of Iteratively Truncated Newton’s Algorithm

Cited by 1 publication

References 12 publications

On TSVD regularization for a Broyden-type algorithm

On TSVD regularization for a Broyden-type algorithm

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