On inverse problems in partially ordered spaces with a priori information

Yury M. Korolev; Anatoly G. Yagola

doi:10.1515/jip-2012-0022

On inverse problems in partially ordered spaces with a priori information

Yury M. Korolev, Anatoly G. Yagola

Department of Mathematical Sciences

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

8 Citations (SciVal)

Abstract

We consider ill-posed inverse problems for linear operator equations Az = u in Banach lattices with a priori information that the exact solution belongs to a compact set. We provide an error estimate for an approximate solution to the ill-posed problem. We also show the existence of a supremum and infimum of the set of approximate solutions and their convergence to the exact solution. After finite-dimensional approximation the problem of computation of the bounds is reduced to a linear programming problem.

Original language	English
Pages (from-to)	567-573
Number of pages	7
Journal	Journal of Inverse and Ill-posed Problems
Volume	20
Issue number	4
DOIs	https://doi.org/10.1515/jip-2012-0022
Publication status	Published - 1 Oct 2012

Bibliographical note

Funding Information:
This work was supported by the Visby program and the RFBR grant 11-01-0090-a.

Funding

This work was supported by the Visby program and the RFBR grant 11-01-0090-a.

Keywords

Error estimation
Ill-posed problems
Partially ordered spaces

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1515/jip-2012-0022Licence: Unspecified

Cite this

@article{34f7e7a50ab0485f91dbdfa9bec47698,

title = "On inverse problems in partially ordered spaces with a priori information",

abstract = "We consider ill-posed inverse problems for linear operator equations Az = u in Banach lattices with a priori information that the exact solution belongs to a compact set. We provide an error estimate for an approximate solution to the ill-posed problem. We also show the existence of a supremum and infimum of the set of approximate solutions and their convergence to the exact solution. After finite-dimensional approximation the problem of computation of the bounds is reduced to a linear programming problem.",

keywords = "Error estimation, Ill-posed problems, Partially ordered spaces",

author = "Korolev, \{Yury M.\} and Yagola, \{Anatoly G.\}",

note = "Funding Information: This work was supported by the Visby program and the RFBR grant 11-01-0090-a.",

year = "2012",

month = oct,

day = "1",

doi = "10.1515/jip-2012-0022",

language = "English",

volume = "20",

pages = "567--573",

journal = "Journal of Inverse and Ill-posed Problems",

issn = "0928-0219",

publisher = "De Gruyter",

number = "4",

}

TY - JOUR

T1 - On inverse problems in partially ordered spaces with a priori information

AU - Korolev, Yury M.

AU - Yagola, Anatoly G.

N1 - Funding Information: This work was supported by the Visby program and the RFBR grant 11-01-0090-a.

PY - 2012/10/1

Y1 - 2012/10/1

N2 - We consider ill-posed inverse problems for linear operator equations Az = u in Banach lattices with a priori information that the exact solution belongs to a compact set. We provide an error estimate for an approximate solution to the ill-posed problem. We also show the existence of a supremum and infimum of the set of approximate solutions and their convergence to the exact solution. After finite-dimensional approximation the problem of computation of the bounds is reduced to a linear programming problem.

AB - We consider ill-posed inverse problems for linear operator equations Az = u in Banach lattices with a priori information that the exact solution belongs to a compact set. We provide an error estimate for an approximate solution to the ill-posed problem. We also show the existence of a supremum and infimum of the set of approximate solutions and their convergence to the exact solution. After finite-dimensional approximation the problem of computation of the bounds is reduced to a linear programming problem.

KW - Error estimation

KW - Ill-posed problems

KW - Partially ordered spaces

UR - http://www.scopus.com/inward/record.url?scp=84869408800&partnerID=8YFLogxK

U2 - 10.1515/jip-2012-0022

DO - 10.1515/jip-2012-0022

M3 - Article

AN - SCOPUS:84869408800

SN - 0928-0219

VL - 20

SP - 567

EP - 573

JO - Journal of Inverse and Ill-posed Problems

JF - Journal of Inverse and Ill-posed Problems

IS - 4

ER -

On inverse problems in partially ordered spaces with a priori information

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this