title: Regularization of the solution of integral equations of the first kind using quadrature formulas
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: 2022-02-16T19:15:02Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-02-16T19:15:02Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Lebedeva A.V., Ryabov V.M. Regularization of the solution of integral equations of the first kind using quadrature formulas. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 4, pp. 593–599.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/35106
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Ill-conditioned systems of linear algebraic equations (SLAEs) and integral equations of the
  first kind belonging to the class of ill-posed problems are considered. 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 SLAEs with special matrices.
  To obtain a reliable solution, regularization methods are used. The general strategy is to
  use the Tikhonov stabilizer or its modifications, or to represent the desired solution in the
  form of an orthogonal the sum of two vectors, one of which is determined stably, and to
  search for the second requires some kind of stabilization procedure. In this article methods
  for the numerical solution of SLAEs with positive a certain symmetric matrix or with an
  oscillatory type matrix using regularization, leading to a SLAE with a reduced condition
  number. A method of reducing the problem of inversion of the integral Laplace transform
  to a SLAE with generalized Vandermonde matrices of oscillation type, the regularization
  of which reduces the ill-conditioning of the system, is indicated.
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).
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 8 (66); Issue 4
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: Regularization of the solution of integral equations of the first kind using quadrature formulas
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 593-599.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/35106/1/593-599.pdf
resources.format: Adobe PDF
resources.size: 260,92 kB