title: Examples of the best piecewise linear approximation with free nodes
metadata.name: dc.contributor.author
metadata.value: Malozemov, Vasilii N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tamasyan, Grigoriy Sh.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:34:50Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:34:50Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Malozemov V.N., Tamasyan G. Sh. Examples of the best piecewise linear approximation with free nodes. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 623–630.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.408
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15130
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In 1957, E. Ya. Remez published a monograph devoted to numerical methods of Chebyshev
  approximations. Particularly, a problem of the best uniform approximation of a function
  convex on an interval with continuous piecewise linear functions with free nodes was considered.
  In 1975, A. M. Vershik, V. N. Malozemov and A. B. Pevnyi developed a general
  approach for constructing the best piecewise polynomial approximations with free nodes.
  The notion of partition with equal deviations was introduced, and it was established that
  such partition exists and generates the best piecewise polynomial approximation. Moreover,
  a numerical method for constructing a partition with equal deviations was proposed.
  In this paper, we give three examples demonstrating how the general approach works when
  solving the problem of the best piecewise linear approximation with free nodes. In the case
  of an arbitrary continuous function, its best piecewise linear approximation in general is
  not continuous. It is continuous when approximating strictly convex and strictly concave
  functions.
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 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Chebyshev approximations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: piecewise linear function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: partition with equal deviations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Examples of the best piecewise linear approximation with free nodes
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 08-Malozemov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15130/1/08-Malozemov.pdf
resources.format: Adobe PDF
resources.size: 271,06 kB