title: About A. N. Tikhonov’s regularized least squares method
metadata.name: dc.contributor.author
metadata.value: Erokhin, Vladimir Ivanovich
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Volkov, Vladimir Viktorovich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-05-18T12:12:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-05-18T12:12:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Erokhin V. I., Volkov V. V. About A. N. Tikhonov’s regularized least squares method. Vestnik of Saint Petersburg University. Applied mathematics. Computer science. Control processes, 2017, volume 13, issue 1, pp. 4–16.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.101
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6348
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The Tikhonov’s regularized least squares method (RLS) and its applications to problems of
  noisy data processing are considered. The starting point of this research is method for solving
  approximate systems of linear algebraic equations (SLAE), proposed by A. N. Tikhonov in
  1980 that he later named ’RLS’. The traditional method of finding sustainable solutions of the
  problems with approximate data is Tikhonov’s regularization: unconditional minimization of
  the smoothing functional. RLS differs from this approach. This method makes use of the solution
  approach to the mathematical programming problem of a special kind. Nowadays RLS has not become a common tool for solving approximate linear systems, and the theory of RLS is not
  well researched. The purpose of the article is to remedy this deficiency. A number of important
  theoretical and practical aspects of RLS are considered. New results are presented. One of
  the results is the method of constructing a model SLAE with the exact right-hand side and
  approximate matrix for which a priori lower bounds for the maximum relative error of RLS are
  achieved. It is shown that, under certain conditions, RLS reduces to the problem of minimizing
  the smoothing functional or to the least squares method or — and this is an unexpected
  result — to the problem of finding a stationary point of smoothing functional with a negative
  regularization parameter. The algebraic transformation which reduces the conditionality of the
  RLS problem to a numerical solution is constructed and substantiated. We propose illustrative
  example of RLS through an applied image restoration problem for an image, registered by a
  device with an inexact point-spread function. The results of computational experiments are
  given. Refs 18. Figs 3.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (проект № 16-31-50016 мол_нр).
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. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: the approximate system of linear algebraic equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: regularized least squares method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: About A. N. Tikhonov’s regularized least squares method
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Erokhin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6348/1/01-Erokhin.pdf
resources.format: Adobe PDF
resources.size: 363,66 kB