Multivariate data fitting using polyharmonic splines

0543150 - MÚ 2022 RIV NL eng J - Journal Article
Segeth, Karel
Multivariate data fitting using polyharmonic splines.
Journal of Computational and Applied Mathematics. Roč. 397, December (2021), č. článku 113651. ISSN 0377-0427. E-ISSN 1879-1778
R&D Projects: GA ČR(CZ) GA18-09628S
Institutional support: RVO:67985840
Keywords : data fitting * polyharmonic spline * spline data approximation * Fourier transform
OECD category: Pure mathematics
Impact factor: 2.872, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.cam.2021.113651

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.
Permanent Link: http://hdl.handle.net/11104/0320427