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Multivariate data fitting using polyharmonic splines
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SYSNO ASEP 0543150 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Multivariate data fitting using polyharmonic splines Author(s) Segeth, Karel (MU-W) RID, SAI, ORCID Article number 113651 Source Title Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
Roč. 397, December (2021)Number of pages 11 s. Language eng - English Country NL - Netherlands Keywords data fitting ; polyharmonic spline ; spline data approximation ; Fourier transform Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA18-09628S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000661869500001 EID SCOPUS 85107069185 DOI 10.1016/j.cam.2021.113651 Annotation The paper is concerned with the use of polyharmonic splines as basis functions in multivariate data fitting. We present several properties of polyharmonic splines and their mutual links: they are commonly used radial basis functions, they are basis functions resulting from the application of a particular smooth approximation procedure, and the form and coefficients of the approximant can be obtained as a solution of a boundary value differential problem for the polyharmonic equation. The construction of the approximant is based on the least squares approach. Approximation of the kind mentioned is often used in practical computation especially with the data measured in 2D and 3D for geographic information systems or computer aided geometric design. The smooth approximation point of view provides the best description of the properties of polyharmonic splines employed for approximation. We mention the connections to interpolation where appropriate. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1016/j.cam.2021.113651
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