Advances in Computational Mathematics

, Volume 2, Issue 1, pp 81–99 | Cite as

Least squares surface approximation to scattered data using multiquadratic functions

  • Richard Franke
  • Hans Hagen
  • Gregory M. Nielson


The paper documents an investigation into some methods for fitting surfaces to scattered data. The form of the fitting function is a multiquadratic function with the criteria for the fit being the least mean squared residual for the data points. The principal problem is the selection of knot points (or base points for the multiquadratic basis functions), although the selection of the multiquadric parameter also plays a nontrivial role in the process. We first describe a greedy algorithm for knot selection, and this procedure is used as an initial step in what follows. The minimization including knot locations and the multiquadric parameter is explored, with some unexpected results in terms of “near repeated” knots. This phenomenon is explored, and leads us to consider variable parameter values for the basis functions. Examples and results are given throughout.


Radial Basis Function Greedy Algorithm Parent Function Scattered Data Parent Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Richard Franke
    • 1
  • Hans Hagen
    • 2
  • Gregory M. Nielson
    • 3
  1. 1.Department of MathematicsNaval Postgraduate SchoolMontereyUSA
  2. 2.FB InformatikUniversität KaiserslauternKaiserlauternGermany
  3. 3.Department of Computer ScienceArizona State UniversityTempeUSA

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