Hermite Interpolation of Multivariable Function Given at Scattered Points

Artur Krowiak 1  and Jordan Podgórski 2
  • 1 Institute of Computer Science, Mechanical faculty, Cracow University of Technology
  • 2 Mechanical faculty, Cracow University of Technology

Abstract

The paper shows the approach to the interpolation of scattered data which includes not only function values, but also values of derivatives of the function. To this end, an interpolant composed of radial basis functions is used and extended by terms possessing appropriate derivative terms. The latter match the given derivatives. Special attention is paid to the problem of choosing the value of the shape parameter, which is included in radial functions and influences the accuracy and stability of the solution. To validate the method, several numerical tests are carried out in the paper.

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