The Hermite-Birkhoff Problem and Local Spline Approximation

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The Hermite-Birkhoff Problem and Local Spline Approximation. / Burova, I.G.

In: WSEAS Transactions on Mathematics, Vol. 23, 02.10.2024, p. 591-598.

Research output: Contribution to journal › Article › peer-review

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Burova, I.G. / The Hermite-Birkhoff Problem and Local Spline Approximation. In: WSEAS Transactions on Mathematics. 2024 ; Vol. 23. pp. 591-598.

BibTeX

@article{8d33970ba5b640e3a17cb95fac9a1a0d,

title = "The Hermite-Birkhoff Problem and Local Spline Approximation",

abstract = "This paper discusses the use of local spline approximations to solve the Hermite-Birkhoff problem. The solution to a specific problem using polynomial and non-polynomial local splines of the third order of approximation is considered. Here we discuss the case when the values of the function u(x) and its derivative u'(x) are given at the nodes of the grid in an alternative way:., u(xj), u'(xj+1), u(xj+2),. Note that when using polynomial and non-polynomial spline approximations, it is possible to obtain acceptable solutions in several interesting cases that are impossible when we use the classical approach. In the case of using local basis splines, many previously unsolvable problems turn out to be solvable. The results of the numerical experiments are presented. {\textcopyright} 2024 World Scientific and Engineering Academy and Society. All rights reserved.",

keywords = "approximation, exponential local splines, Hermite interpolation, Hermite-Birkhoff interpolation, Lagrange interpolation, non-polynomial local splines, polynomial local splines",

author = "I.G. Burova",

note = "Export Date: 21 October 2024 Адрес для корреспонденции: Burova, I.G.; The Department of Computational Mathematics, 7-9 Universitetskaya Embankment, Russian Federation",

year = "2024",

month = oct,

day = "2",

doi = "10.37394/23206.2024.23.62",

language = "Английский",

volume = "23",

pages = "591--598",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - The Hermite-Birkhoff Problem and Local Spline Approximation

AU - Burova, I.G.

N1 - Export Date: 21 October 2024 Адрес для корреспонденции: Burova, I.G.; The Department of Computational Mathematics, 7-9 Universitetskaya Embankment, Russian Federation

PY - 2024/10/2

Y1 - 2024/10/2

N2 - This paper discusses the use of local spline approximations to solve the Hermite-Birkhoff problem. The solution to a specific problem using polynomial and non-polynomial local splines of the third order of approximation is considered. Here we discuss the case when the values of the function u(x) and its derivative u'(x) are given at the nodes of the grid in an alternative way:., u(xj), u'(xj+1), u(xj+2),. Note that when using polynomial and non-polynomial spline approximations, it is possible to obtain acceptable solutions in several interesting cases that are impossible when we use the classical approach. In the case of using local basis splines, many previously unsolvable problems turn out to be solvable. The results of the numerical experiments are presented. © 2024 World Scientific and Engineering Academy and Society. All rights reserved.

AB - This paper discusses the use of local spline approximations to solve the Hermite-Birkhoff problem. The solution to a specific problem using polynomial and non-polynomial local splines of the third order of approximation is considered. Here we discuss the case when the values of the function u(x) and its derivative u'(x) are given at the nodes of the grid in an alternative way:., u(xj), u'(xj+1), u(xj+2),. Note that when using polynomial and non-polynomial spline approximations, it is possible to obtain acceptable solutions in several interesting cases that are impossible when we use the classical approach. In the case of using local basis splines, many previously unsolvable problems turn out to be solvable. The results of the numerical experiments are presented. © 2024 World Scientific and Engineering Academy and Society. All rights reserved.

KW - approximation

KW - exponential local splines

KW - Hermite interpolation

KW - Hermite-Birkhoff interpolation

KW - Lagrange interpolation

KW - non-polynomial local splines

KW - polynomial local splines

UR - https://www.mendeley.com/catalogue/66b90b69-ba1a-3a28-a324-86f67effce77/

U2 - 10.37394/23206.2024.23.62

DO - 10.37394/23206.2024.23.62

M3 - статья

VL - 23

SP - 591

EP - 598

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 126220903