Abstract
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 illustratethem.
Highlights
Measuring data of all different types and formats is the basic means of research in all branches of science and technology
We are concerned with the problem of data interpolation in an arbitrary dimension
The background of the paper is the so-called smooth interpolation [1], [2] allowing for the minimization of some functionals applied to the interpolation formula
Summary
Measuring data of all different types and formats is the basic means of research in all branches of science and technology. Choosing particular basis functions in the minimization space, we can get an interpolation formula whose principal part is a linear combination of polyharmonic splines of fixed order that are, at the same time, radial functions. We construct such a radial basis, i.e. polyharmonic splines, and show its properties.
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