Errors of approximation with polynomial splines of the fifth order

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Abstract

This paper is a continuation of a series of papers devoted to the construction and investigation of the properties of integro-differential polynomial splines of the fifth order. It is supposed that values of function in grid nodes and values of integrals over intervals are known. Solving the system of linear algebraic equations, we find basic splines. An approximation of the function in this paper is constructed on every grid interval separately using values of the function in two adjacent grid nodes and the values of three integrals over intervals, and basic splines. We call this approximation an integro-differential spline and we call these basic splines integro-differential basic splines. The properties of interpolation with integro-differential polynomial basic splines are investigated. A comparison of the properties of integro-differential approximations for a different choice of integrals is presented. A comparison of the integro-differential approximation with approximation using polynomial splines of the Lagrangian type is made. Numerical examples are presented.

Original languageEnglish
Title of host publicationApplied Physics, System Science and Computers II
Subtitle of host publicationProceedings of the 2nd International Conference on Applied Physics, System Science and Computers (APSAC2017), September 27-29, 2017, Dubrovnik, Croatia
EditorsKlimis Ntalianis, Anca Croitoru
PublisherSpringer Nature
Pages39-46
Number of pages8
ISBN (Electronic)978-3-319-75605-9
ISBN (Print)978-3-319-75604-2
DOIs
StatePublished - 1 Jan 2019
Event2nd International Conference on Applied Physics, System Science and Computers - Dubrovnik, Croatia
Duration: 27 Sep 201729 Sep 2017

Publication series

NameLNEE
PublisherSpringer Nature
Volume489
ISSN (Print)1876-1100

Conference

Conference2nd International Conference on Applied Physics, System Science and Computers
Abbreviated titleAPSAC2017
CountryCroatia
CityDubrovnik
Period27/09/1729/09/17

Scopus subject areas

  • Industrial and Manufacturing Engineering

Keywords

  • Approximation
  • Integro-differential splines

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