# Errors of approximation with polynomial splines of the fifth order

Research output: Contribution to journalArticleResearchpeer-review

### 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 language English 39-46 8 Lecture Notes in Electrical Engineering 489 https://doi.org/10.1007/978-3-319-75605-9_6 Published - 1 Jan 2019

### Keywords

• Approximation
• Integro-differential splines

### Scopus subject areas

• Industrial and Manufacturing Engineering

### Cite this

@article{2686d8158ea4448d8b7f999ea637d696,
title = "Errors of approximation with polynomial splines of the fifth order",
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.",
keywords = "Approximation, Integro-differential splines",
author = "Бурова, {Ирина Герасимовна} and Доронина, {Александра Геннадьевна}",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/978-3-319-75605-9_6",
language = "English",
volume = "489",
pages = "39--46",
journal = "Lecture Notes in Electrical Engineering",
issn = "1876-1100",
publisher = "Springer",

}

In: Lecture Notes in Electrical Engineering, Vol. 489, 01.01.2019, p. 39-46.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Errors of approximation with polynomial splines of the fifth order

AU - Бурова, Ирина Герасимовна

AU - Доронина, Александра Геннадьевна

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Approximation

KW - Integro-differential splines

UR - http://www.scopus.com/inward/record.url?scp=85049316320&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-75605-9_6

DO - 10.1007/978-3-319-75605-9_6

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VL - 489

SP - 39

EP - 46

JO - Lecture Notes in Electrical Engineering

JF - Lecture Notes in Electrical Engineering

SN - 1876-1100

ER -