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Article

Segeth, Karel
Multivariate smooth interpolation that employs polyharmonic functions. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 24-29, 2018. Institute of Mathematics CAS, Prague, 2019. pp. 140-148
MSC: 31B30, 41A05, 41A63, 42A38, 65D05 | DOI: 10.21136/panm.2018.15
Keywords:
data interpolation; smooth interpolation; polyharmonic spline; radial basis function; Fourier transform
Summary:
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g.\ in geographic information systems or computer aided geometric design. A simple computational example is presented.
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