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C 1 surface interpolation with constraints

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Abstract

Givenn pairwise distinct and arbitrarily spaced pointsP i in a domainD of thex−y plane andn real numbersf i, consider the problem of computing a bivariate functionf(x, y) of classC 1 inD whose values inP i are exactlyf i,i=1,…,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ l inD.

In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.

The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.

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References

  1. R.E. Barnhill, G. Birkhoff and W.J. Gordon, Smooth interpolation in triangles, J. Approx. Theory 8 (1973) 114–128.

    Google Scholar 

  2. R.E. Barnhill and J.A. Gregory, Compatible smooth interpolation in triangles, J. Approx. Theory 15 (1975) 214–225.

    Google Scholar 

  3. M.R. Hestenes,Optimization Theory. The Finite Dimensional Case (Wiley, New York, 1975).

    Google Scholar 

  4. A.S. Householder,The Theory of Matrices in Numerical Analysis (Blaisdell, New York, 1964).

    Google Scholar 

  5. I. Kaneko and R. Plemmons, Minimum norm solutions to linear elastic analysis problems, Int. J. Numer. Meth. Eng. 20 (1984) 983–998.

    Google Scholar 

  6. I.M. Klucewicz, A piecewiseC 1 interpolant to arbitrarily spaced data, Comp. Graphics and Image Processing 8 (1978) 92–112.

    Google Scholar 

  7. C.L. Lawson, Software forC 1 surface interpolation, in:Mathematical Software III, ed. J.R. Rice (Academic Press, New York, 1977).

    Google Scholar 

  8. G.M. Nielson, A method for interpolating scattered data based upon a minimum norm network, Math. Comp. 40 (1983) 253–271.

    Google Scholar 

  9. R.S. Varga,Matrix Iterative Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1962).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Modena, Italy

    Emanuele Galligani

Authors
  1. Emanuele Galligani
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Additional information

Work supported by MURST Project of Computational Mathematics, Italy.

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Galligani, E. C 1 surface interpolation with constraints. Numer Algor 5, 549–555 (1993). https://doi.org/10.1007/BF02113890

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  • DOI: https://doi.org/10.1007/BF02113890

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