title: Regularization of the procedure for inverting the Laplace transform 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: 2022-12-27T14:48:38Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-12-27T14:48:38Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Lebedeva A. V., Ryabov V.M. Regularization of the procedure for inverting the Laplace transform using quadrature formulas. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 4, pp. 636–643. https://doi.org/10.21638/spbu01.2022.406 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.406
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38720
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of inversion of the integral Laplace transform, which belongs to the class of
  ill-posed problems, is considered. Integral equations are reduced to ill-conditioned systems
  of linear algebraic equations (SLAE), in which the unknowns are either the expansion coefficients
  in a series in terms of shifted Legendre polynomials, or the approximate values of
  the desired original at a number of points. The first step of reduction to SLAE is to apply
  quadrature formulas that provide the minimum values of the condition number of SLAE.
  Regularization methods are used to obtain a reliable solution of the system. A common
  strategy is to use the Tikhonov stabilizer or its modifications. A variant of the regularization
  method for systems with oscillatory-type matrices is presented, which significantly
  reduces the conditionality of the problem in comparison with the classical Tikhonov scheme.
  A method is given for actually constructing special quadratures leading to problems with
  oscillation matrices.
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 9 (67); 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: oscillation matrices
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 procedure for inverting the Laplace transform using quadrature formulas
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 636-643.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38720/1/636-643.pdf
resources.format: Adobe PDF
resources.size: 265,25 kB