Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

Y. Zhang; D. V. Lukyanenko; A. G. Yagola

doi:10.1080/17415977.2015.1077445

Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

Y. Zhang^*, D. V. Lukyanenko, A. G. Yagola

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

Original language	English
Pages (from-to)	811-831
Number of pages	21
Journal	Inverse Problems in Science and Engineering
Volume	24
Issue number	5
DOIs	https://doi.org/10.1080/17415977.2015.1077445
Publication status	Published - 12 Jun 2016
Externally published	Yes

Keywords

Fredholm integral equation of the first kind
Lagrange principle
error estimation
optimal recovery
regularization

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10.1080/17415977.2015.1077445

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title = "Using Lagrange principle for solving two-dimensional integral equation with a positive kernel",

abstract = "This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.",

keywords = "Fredholm integral equation of the first kind, Lagrange principle, error estimation, optimal recovery, regularization",

author = "Y. Zhang and Lukyanenko, {D. V.} and Yagola, {A. G.}",

note = "Publisher Copyright: {\textcopyright} 2015 Taylor & Francis.",

year = "2016",

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AU - Zhang, Y.

AU - Lukyanenko, D. V.

AU - Yagola, A. G.

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Y1 - 2016/6/12

N2 - This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

AB - This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

KW - Fredholm integral equation of the first kind

KW - Lagrange principle

KW - error estimation

KW - optimal recovery

KW - regularization

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JO - Inverse Problems in Science and Engineering

JF - Inverse Problems in Science and Engineering

IS - 5

ER -

Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

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Keywords

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