Polyharmonic splines generated by multivariate smooth interpolation
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Polyharmonic splines generated by multivariate smooth interpolation
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-09628S" target="_blank" >GA18-09628S: Advanced flow-field analysis</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computers & Mathematics With Applications
ISSN
0898-1221
e-ISSN
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Volume of the periodical
78
Issue of the periodical within the volume
9
Country of publishing house
GB - UNITED KINGDOM
Number of pages
10
Pages from-to
3067-3076
UT code for WoS article
000491624900015
EID of the result in the Scopus database
2-s2.0-85065032844