Optimal Multivariate Interpolation

  • Tobias Werther
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 7)


In this chapter, we are concerned with the problem of multivariate data interpolation. The main focus lies on the concept of minimizing a quadratic form which, in practice, emerges from a physical model, subject to the interpolation constraints. The approach is a natural extension of the one-dimensional polynomial spline interpolation. Besides giving a basic outline of the mathematical framework, we design a fast numerical scheme and analyze the performance quality. We finally show that optimal interpolation is closely related to standard linear stochastic estimation methods.


Interpolation Problem Thin Plate Spline Optimal Interpolation Relative Absolute Error Linear Unbiased Prediction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Tobias Werther
    • 1
  1. 1.Department of MathematicsUniversity of ViennaAustria

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