I. E. Svetov, A. P. Polyakova, “Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography”, Sib. Èlektron. Mat. Izv., 10 (2013), 90

Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]

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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2013, Volume 10, Pages 90–108 (Mi semr400)

This article is cited in 10 scientific papers (total in 10 papers)

Computational mathematics

Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography

I. E. Svetov^ab, A. P. Polyakova^a

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

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Abstract: We compare two algorithms for reconstruction the vector fields from the known values of the ray transforms. The first algorithm is based on the least square method, approximating sequence is constructed with using the $B$-splines. The second algorithm is based on the method of singular value decomposition of operators of ray transforms, basis vector fields are constructed with using the harmonic polynomials and Jacobi polynomials.

Keywords: vector tomography, solenoidal field, potential field, approximation, ray transforms, least square method, $B$-splines, singular value decomposition, orthogonal polynomials.

Received August 25, 2012, published February 15, 2013

Document Type: Article

UDC: 514.8, 517.983, 519.6

MSC: 44A30

Language: Russian

Citation: I. E. Svetov, A. P. Polyakova, “Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography”, Sib. Èlektron. Mat. Izv., 10 (2013), 90–108

Citation in format AMSBIB

\Bibitem{SvePol13}

\by I.~E.~Svetov, A.~P.~Polyakova

\paper Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography

\jour Sib. \`Elektron. Mat. Izv.

\yr 2013

\vol 10

\pages 90--108

\mathnet{http://mi.mathnet.ru/semr400}

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https://www.mathnet.ru/eng/semr/v10/p90

This publication is cited in the following 10 articles:

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