Abstract

This paper is devoted to the processing of large numerical signals which arise in different technical problems (for example, in positioning systems, satellite maneuvers, in the prediction a lot of phenomenon, and so on). The main tool of the processing is polynomial and nonpolynomial splines of the Hermite type, which are obtained by the approximation relations. These relations allow us to construct splines with approximate properties, which are asymptotically optimal as to N-width of the standard compact sets. The interpolation properties of the mentioned splines are investigated. Such properties give opportunity to obtain the solution of the interpolation Hermite problems without solution of equation systems. The calibration relations on embedded grids are established in the case of deleting the grid knots and in the case of the addition of the last one. A consequence of the obtained results is the embedding of the Hermite spline spaces on the embedded grids. The mentioned embedding allows us to obtain wavelet decomposition of the Hermite spline spaces.

Original languageEnglish
Pages (from-to)222-234
Number of pages13
JournalWSEAS Transactions on Applied and Theoretical Mechanics
Volume14
Publication statusPublished - 1 Jan 2019

Fingerprint

Splines
Interpolation
Wavelet decomposition
Processing
Polynomials
Satellites
Calibration

Scopus subject areas

  • Computational Mechanics
  • Civil and Structural Engineering
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

@article{c682b001a8304a90aaa2a5fc8707139e,
title = "Embedded spaces of hermite splines",
abstract = "This paper is devoted to the processing of large numerical signals which arise in different technical problems (for example, in positioning systems, satellite maneuvers, in the prediction a lot of phenomenon, and so on). The main tool of the processing is polynomial and nonpolynomial splines of the Hermite type, which are obtained by the approximation relations. These relations allow us to construct splines with approximate properties, which are asymptotically optimal as to N-width of the standard compact sets. The interpolation properties of the mentioned splines are investigated. Such properties give opportunity to obtain the solution of the interpolation Hermite problems without solution of equation systems. The calibration relations on embedded grids are established in the case of deleting the grid knots and in the case of the addition of the last one. A consequence of the obtained results is the embedding of the Hermite spline spaces on the embedded grids. The mentioned embedding allows us to obtain wavelet decomposition of the Hermite spline spaces.",
keywords = "Hermite problem, Non-polynomial splines, Polynomial splines",
author = "Dem’Yanovich, {Yu K.} and Burova, {I. G.} and Evdokimova, {T. O.} and Lebedeva, {A. V.} and Doronina, {A. G.}",
year = "2019",
month = "1",
day = "1",
language = "English",
volume = "14",
pages = "222--234",
journal = "WSEAS Transactions on Applied and Theoretical Mechanics",
issn = "1991-8747",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

TY - JOUR

T1 - Embedded spaces of hermite splines

AU - Dem’Yanovich, Yu K.

AU - Burova, I. G.

AU - Evdokimova, T. O.

AU - Lebedeva, A. V.

AU - Doronina, A. G.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This paper is devoted to the processing of large numerical signals which arise in different technical problems (for example, in positioning systems, satellite maneuvers, in the prediction a lot of phenomenon, and so on). The main tool of the processing is polynomial and nonpolynomial splines of the Hermite type, which are obtained by the approximation relations. These relations allow us to construct splines with approximate properties, which are asymptotically optimal as to N-width of the standard compact sets. The interpolation properties of the mentioned splines are investigated. Such properties give opportunity to obtain the solution of the interpolation Hermite problems without solution of equation systems. The calibration relations on embedded grids are established in the case of deleting the grid knots and in the case of the addition of the last one. A consequence of the obtained results is the embedding of the Hermite spline spaces on the embedded grids. The mentioned embedding allows us to obtain wavelet decomposition of the Hermite spline spaces.

AB - This paper is devoted to the processing of large numerical signals which arise in different technical problems (for example, in positioning systems, satellite maneuvers, in the prediction a lot of phenomenon, and so on). The main tool of the processing is polynomial and nonpolynomial splines of the Hermite type, which are obtained by the approximation relations. These relations allow us to construct splines with approximate properties, which are asymptotically optimal as to N-width of the standard compact sets. The interpolation properties of the mentioned splines are investigated. Such properties give opportunity to obtain the solution of the interpolation Hermite problems without solution of equation systems. The calibration relations on embedded grids are established in the case of deleting the grid knots and in the case of the addition of the last one. A consequence of the obtained results is the embedding of the Hermite spline spaces on the embedded grids. The mentioned embedding allows us to obtain wavelet decomposition of the Hermite spline spaces.

KW - Hermite problem

KW - Non-polynomial splines

KW - Polynomial splines

UR - http://www.scopus.com/inward/record.url?scp=85073693576&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85073693576

VL - 14

SP - 222

EP - 234

JO - WSEAS Transactions on Applied and Theoretical Mechanics

JF - WSEAS Transactions on Applied and Theoretical Mechanics

SN - 1991-8747

ER -