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

This article is cited in 9 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

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.

UDC: 514.8, 517.983, 519.6

MSC: 44A30

Received August 25, 2012, published February 15, 2013