Multivariate interpolation using polyharmonic splines

0540785 - MÚ 2022 RIV CZ eng J - Journal Article
Segeth, Karel
Multivariate interpolation using polyharmonic splines.
Acta Polytechnica. Roč. 61, SI (2021), s. 148-154. ISSN 1210-2709. E-ISSN 1805-2363
R&D Projects: GA ČR(CZ) GA18-09628S
Institutional support: RVO:67985840
Keywords : data interpolation * Fourier transform * polyharmonic spline * smooth interpolation
OECD category: Pure mathematics
Method of publishing: Open access
https://doi.org/10.14311/AP.2021.61.0148

Data measuring and further processing is the fundamental activity in all branches of science and technology. Data interpolation has been an important part of computational mathematics for a long time. In the paper, we are concerned with the interpolation by polyharmonic splines in an arbitrary dimension. We show the connection of this interpolation with the interpolation by radial basis functions and the smooth interpolation by generating functions, which provide means for minimizing the L2 norm of chosen derivatives of the interpolant. This can be useful in 2D and 3D, e.g., in the construction of geographic information systems or computer aided geometric design. We prove the properties of the piecewise polyharmonic spline interpolant and present a simple 1D example to illustrate them.
Permanent Link: http://hdl.handle.net/11104/0318383