title: Method of moments in the problem of inversion of the Laplace transform and its regularization
metadata.name: dc.contributor.author
metadata.value: Lebedeva, Anastasia V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ryabov, Victor M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-04-14T11:09:42Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-04-14T11:09:42Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.105
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/36153
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: 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).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: system of linear algebraic equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral equations of the first kind
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ill-posed problems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ill-conditioned problems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: condition number
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: regularization method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Method of moments in the problem of inversion of the Laplace transform and its regularization
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 46-52.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/36153/1/46-52.pdf
resources.format: Adobe PDF
resources.size: 412,98 kB