title: On the numerical solution of system of linear algebraic equations with ill-conditioned matrices
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: 2019-12-06T12:06:06Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-12-06T12:06:06Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Lebedeva A.V., Ryabov V.M. On the numerical solution of system of linear algebraic equations with ill-conditioned matrices. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 4, pp. 619–626.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.407
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16744
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The system of linear algebraic equations (SLAE) is considered. If the matrix of the system
  is non-degenerate, then there is a unique solution to the system. In a degenerate case, the
  system may not have a solution or have infinitely many solutions. In this case, the concept
  of a normal solution is introduced. The case of a non-degenerate square matrix can theoretically
  be considered good in terms of existence and uniqueness of the solution, but in
  the theory of computational methods, nondegenerate matrices are divided into two categories:
  “ill-conditioned” and “well-conditioned”. Badly called matrices for which the solution of the system of equations is practically unstable. One of the important characteristics of
  practical solution stability A system of linear equations is a condition number. Usually,
  regularization methods are used to obtain a reliable solution. A common strategy is to use
  Tikhonov’s stabilizer or his modifications, or the representation of the desired solution in
  the form of orthogonal sums of two vectors, one of which is determined stably, and for
  searching the second requires some stabilization procedure. In this article the methods of
  numerical solution of SLAE are considered with a positive defined symmetric matrix or oscillating
  matrix type using regularization, leading to SLAEs with a reduced conditionality
  number.
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 6 (64); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: a system of linear algebraic equations
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: On the numerical solution of system of linear algebraic equations with ill-conditioned matrices
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 619-626.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16744/1/619-626.pdf
resources.format: Adobe PDF
resources.size: 269,82 kB