Convergence of spline interpolation processes and conditionality of systems of equations for spline construction

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Convergence of spline interpolation processes and conditionality of systems of equations for spline construction. / Volkov, Y. S.

In: Sbornik Mathematics, Vol. 210, No. 4, 04.2019, p. 550-564.

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

BibTeX

@article{d303287931ce49fba9ac0aaf8607fc26,

title = "Convergence of spline interpolation processes and conditionality of systems of equations for spline construction",

abstract = "This study is a continuation of research on the convergence of interpolation processes with classical polynomial splines of odd degree. It is proved that the problem of good conditionality of a system of equations for interpolation spline construction via coefficients of the expansion of the kth derivative in B-splines is equivalent to the problem of convergence of the interpolation process for the Kth spline derivative in the class of functions with continuous Kth derivatives. It is established that for interpolation with splines of degree 2n - 1, the conditions that the projectors corresponding to the derivatives of orders k and 2n - 1 - k be bounded are equivalent. Bibliography: 26 titles.",

keywords = "Conditionality, Construction algorithms, Convergence, Interpolation, Projector norm, Splines, construction algorithms, convergence, projector norm, conditionality, BAND MATRICES, splines, INVERSES, interpolation, NORM",

author = "Volkov, {Y. S.}",

year = "2019",

month = apr,

doi = "10.1070/SM8964",

language = "English",

volume = "210",

pages = "550--564",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "4",

}

RIS

TY - JOUR

T1 - Convergence of spline interpolation processes and conditionality of systems of equations for spline construction

AU - Volkov, Y. S.

PY - 2019/4

Y1 - 2019/4

N2 - This study is a continuation of research on the convergence of interpolation processes with classical polynomial splines of odd degree. It is proved that the problem of good conditionality of a system of equations for interpolation spline construction via coefficients of the expansion of the kth derivative in B-splines is equivalent to the problem of convergence of the interpolation process for the Kth spline derivative in the class of functions with continuous Kth derivatives. It is established that for interpolation with splines of degree 2n - 1, the conditions that the projectors corresponding to the derivatives of orders k and 2n - 1 - k be bounded are equivalent. Bibliography: 26 titles.

AB - This study is a continuation of research on the convergence of interpolation processes with classical polynomial splines of odd degree. It is proved that the problem of good conditionality of a system of equations for interpolation spline construction via coefficients of the expansion of the kth derivative in B-splines is equivalent to the problem of convergence of the interpolation process for the Kth spline derivative in the class of functions with continuous Kth derivatives. It is established that for interpolation with splines of degree 2n - 1, the conditions that the projectors corresponding to the derivatives of orders k and 2n - 1 - k be bounded are equivalent. Bibliography: 26 titles.

KW - Conditionality

KW - Construction algorithms

KW - Convergence

KW - Interpolation

KW - Projector norm

KW - Splines

KW - construction algorithms

KW - convergence

KW - projector norm

KW - conditionality

KW - BAND MATRICES

KW - splines

KW - INVERSES

KW - interpolation

KW - NORM

UR - http://www.scopus.com/inward/record.url?scp=85071112315&partnerID=8YFLogxK

U2 - 10.1070/SM8964

DO - 10.1070/SM8964

M3 - Article

AN - SCOPUS:85071112315

VL - 210

SP - 550

EP - 564

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 4

ER -

ID: 21336475