I. E. Svetov, A. P. Polyakova, S. V. Maltseva, “The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields”, Sib. Zh. Ind. Mat., 22:1 (2019), 104–115; J. Appl. Industr. Math., 13:1 (2019), 157

Sibirskii Zhurnal Industrial'noi Matematiki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Sib. Zh. Ind. Mat.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 1, Pages 104–115
DOI: https://doi.org/10.33048/sibjim.2019.22.110 (Mi sjim1036)

This article is cited in 5 scientific papers (total in 5 papers)

The method of approximate inverse for ray transform operators on two-dimensional symmetric

$m$ -tensor fields

I. E. Svetov^ab, A. P. Polyakova^ab, S. V. Maltseva^abc

^a Sobolev Institute of Mathematics SB RAS, pr. Akad. Koptyuga 4, 630090 Novosibirsk
^b Novosibirsk State University, ul. Pirogova 2, 630090 Novosibirsk
^c Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentyeva 15, 630090 Novosibirsk

Full-text PDF (265 kB) Citations (5)

References:

PDF

HTML

DOI: https://doi.org/10.33048/sibjim.2019.22.110

Abstract: Two approaches are proposed for recovering a symmetric

$m$ -tensor field in a unit disk from the given values of ray transforms. The approaches are based on the method of approximate inverse. The first approach allows us to reconstruct all components of the tensor field, while the second recovers the potentials of the solenoidal part and

$m$ potential parts of the tensor field.

Keywords: tensor tomography, method of approximate inverse, adjoint operator, ray transform, Radon transform, tensor field, potential.

Funding agency	Grant number
Siberian Branch of Russian Academy of Sciences	I.1.5 (проект 0314-2016-0011)
Russian Foundation for Basic Research	18-01-00057_а

Received: 09.06.2018
Revised: 24.10.2018
Accepted: 15.12.2018

English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 1, Pages 157–167
DOI: https://doi.org/10.1134/S1990478919010162

Bibliographic databases:

Document Type: Article

UDC: 517.98:519.677

Language: Russian

Citation: I. E. Svetov, A. P. Polyakova, S. V. Maltseva, “The method of approximate inverse for ray transform operators on two-dimensional symmetric

$m$ -tensor fields”, Sib. Zh. Ind. Mat., 22:1 (2019), 104–115; J. Appl. Industr. Math., 13:1 (2019), 157–167

Citation in format AMSBIB

\Bibitem{SvePolMal19}

\by I.~E.~Svetov, A.~P.~Polyakova, S.~V.~Maltseva

\paper The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields

\jour Sib. Zh. Ind. Mat.

\yr 2019

\vol 22

\issue 1

\pages 104--115

\mathnet{http://mi.mathnet.ru/sjim1036}

\crossref{https://doi.org/10.33048/sibjim.2019.22.110}

\elib{https://elibrary.ru/item.asp?id=38683430}

\transl

\jour J. Appl. Industr. Math.

\yr 2019

\vol 13

\issue 1

\pages 157--167

\crossref{https://doi.org/10.1134/S1990478919010162}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064909425}

Linking options:

https://www.mathnet.ru/eng/sjim1036

https://www.mathnet.ru/eng/sjim/v22/i1/p104

This publication is cited in the following 5 articles:

I. E. Svetov, A. P. Polyakova, “Decomposition of symmetric tensor fields in $\mathbb{R}^3$”, J. Appl. Industr. Math., 17:1 (2023), 199–212
I E Svetov, A P Polyakova, “The method of approximate inverse for the normal Radon transform operator”, J. Phys.: Conf. Ser., 1715:1 (2021), 012048
A K Louis, S V Maltseva, A P Polyakova, T Schuster, I E Svetov, “On solving the slice-by-slice three-dimensional 2-tensor tomography problems using the approximate inverse method”, J. Phys.: Conf. Ser., 1715:1 (2021), 012036
A P Polyakova, I E Svetov, “The singular value decomposition of the dynamic ray transforms operators acting on 2-tensor fields in ℝ2”, J. Phys.: Conf. Ser., 1715:1 (2021), 012040
I. E. Svetov, “the Method of Approximate Inverse For the Radon Transform Operator Acting on Functions and For the Normal Radon Transform Operators Acting on Vector and Symmetric 2-Tensor Fields in R-3”, Sib. Electron. Math. Rep., 17 (2020), 1073–1087

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Сибирский журнал индустриальной математики

Statistics & downloads:
Abstract page:	297
Full-text PDF :	95
References:	41
First page:	3

Что такое QR-код?

Registration to the website

Logotypes