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DC Field | Value | Language |
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dc.contributor.author | Lebedeva, Anastasia V. | - |
dc.contributor.author | Ryabov, Victor M. | - |
dc.date.accessioned | 2022-04-14T11:09:42Z | - |
dc.date.available | 2022-04-14T11:09:42Z | - |
dc.date.issued | 2022-03 | - |
dc.identifier.citation | Lebedeva A.V., Ryabov V.M. Method of moments in the problem of inversion of the Laplace transform and its regularization. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 1, pp. 46–52. | en_GB |
dc.identifier.other | https://doi.org/10.21638/spbu01.2022.105 | - |
dc.identifier.uri | http://hdl.handle.net/11701/36153 | - |
dc.description.abstract | Integral equations of the first kind are considered, which belong to the class of ill-posed problems. This also includes the problem of inverting the integral Laplace transform, which is used to solve a wide class of mathematical problems. Integral equations are reduced to illconditioned systems of linear algebraic equations, in which the unknowns are the coefficients of the expansion in a series in the shifted Legendre polynomials of some function that simply expresses in terms of the sought original. This function is found as a solution to a certain finite moment problem in a Hilbert space. To obtain a reliable solution to the system, regularization methods are used. The general strategy is to use the Tikhonov stabilizer or its modifications. A specific type of stabilizer in the regularization method is indicated, focused on a priori low degree of smoothness of the desired original. The results of numerical experiments are presented, confirming the effectiveness of the proposed inversion algorithm. | en_GB |
dc.description.sponsorship | This paper was prepared with the support by a grant from St Petersburg State University (Event 3, Pure ID 75207094). Research was carried out using computational resources provided by Resource Center “Computer Center of SPbU” (http://www.cc.spbu.ru/en). | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9; Issue 1 | - |
dc.subject | system of linear algebraic equations | en_GB |
dc.subject | integral equations of the first kind | en_GB |
dc.subject | ill-posed problems | en_GB |
dc.subject | ill-conditioned problems | en_GB |
dc.subject | condition number | en_GB |
dc.subject | regularization method | en_GB |
dc.title | Method of moments in the problem of inversion of the Laplace transform and its regularization | en_GB |
dc.type | Article | en_GB |
Appears in Collections: | Issue 1 |
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