Polyharmonic splines generated by multivariate smooth interpolation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00509204" target="_blank" >RIV/67985840:_____/19:00509204 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.camwa.2019.04.018" target="_blank" >http://dx.doi.org/10.1016/j.camwa.2019.04.018</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2019.04.018" target="_blank" >10.1016/j.camwa.2019.04.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polyharmonic splines generated by multivariate smooth interpolation

Popis výsledku v původním jazyce

Polyharmonic splines of order m satisfy the polyharmonic equation of order m in n variables. Moreover, if employed as basis functions for interpolation they are radial functions. We are concerned with the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints for n≥1. This is the principal motivation of the paper. We show a particular procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines of a fixed order, possibly complemented with lower order polynomial terms. If it is advantageous for the interpolant in the problem solved to be a polyharmonic spline we can construct such an interpolant directly using the multivariate smooth approximation technique. The smoothness of the spline can be a priori chosen. Smooth interpolation can be very useful e.g. in signal processing, computer aided geometric design or construction of geographic information systems. A 1D computational example is presented.

Název v anglickém jazyce

Polyharmonic splines generated by multivariate smooth interpolation

Popis výsledku anglicky

Polyharmonic splines of order m satisfy the polyharmonic equation of order m in n variables. Moreover, if employed as basis functions for interpolation they are radial functions. We are concerned with the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints for n≥1. This is the principal motivation of the paper. We show a particular procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines of a fixed order, possibly complemented with lower order polynomial terms. If it is advantageous for the interpolant in the problem solved to be a polyharmonic spline we can construct such an interpolant directly using the multivariate smooth approximation technique. The smoothness of the spline can be a priori chosen. Smooth interpolation can be very useful e.g. in signal processing, computer aided geometric design or construction of geographic information systems. A 1D computational example is presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-09628S" target="_blank" >GA18-09628S: Pokročilá analýza proudových polí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computers & Mathematics With Applications

ISSN

0898-1221

e-ISSN

—

Svazek periodika

78

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

3067-3076

Kód UT WoS článku

000491624900015

EID výsledku v databázi Scopus

2-s2.0-85065032844