Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

A method for interpolating scattered data based upon a minimum norm network


Author: Gregory M. Nielson
Journal: Math. Comp. 40 (1983), 253-271
MSC: Primary 65D05; Secondary 41A05, 65D07
DOI: https://doi.org/10.1090/S0025-5718-1983-0679444-7
MathSciNet review: 679444
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A method for interpolating scattered data is described. Given $ ({x_i},{y_i},{z_i}),i = 1, \ldots, N$, a bivariate function S with continuous first order partial derivatives is defined which has the property that $ S({x_i},{y_i}) = {z_i},i = 1, \ldots ,N$. The method is based upon a triangulation of the domain and a curve network which has certain minimum pseudonorm properties. Algorithms and examples are included.


References [Enhancements On Off] (What's this?)

  • [1] Hiroshi Akima, "A method of bivariate interpolation and smooth surface fitting for values given at irregularly distributed points," Trans. Math. Software, v. 4, 1978, pp. 148-159.
  • [2] Robert E. Barnhill, Representation and approximation of surfaces, Mathematical software, III (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1977) Academic Press, New York, 1977, pp. 69–120. Publ. Math. Res. Center Univ. Wisconsin, No. 39. MR 0489081
  • [3] R. E. Barnhill, G. Birkhoff, and W. J. Gordon, Smooth interpolation in triangles, J. Approximation Theory 8 (1973), 114–128. Collection of articles dedicated to Isaac Jacob Schoenberg on his 70th birthday, II. MR 0368382
  • [4] Carl de Boor and Robert E. Lynch, On splines and their minimum properties, J. Math. Mech. 15 (1966), 953–969. MR 0203306
  • [5] Richard Franke, A Critical Comparison of Some Methods for Interpolation of Scattered Data, Naval Postgraduate School Technical Report NPS-53-79-003, December 1979.
  • [6] R. L. Laney, L. W. Pankratz & C. Zenone, Private Communication, Phoenix, Arizona, 1978.
  • [7] C. L. Lawson, "Software for $ {C^1}$ surface interpolation," Mathematical Software III (J. R. Rice, ed.), Academic Press, New York, 1977, pp. 161-194.
  • [8] B. A. Lewis & J. S. Robinson, "Triangulation of planar regions with applications," Comput. J., v. 21, 1978, pp. 324-332.
  • [9] G. Nielson, Minimum norm interpolation in triangles, SIAM J. Numer. Anal. 17 (1980), no. 1, 44–62. MR 559461, https://doi.org/10.1137/0717007

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D05, 41A05, 65D07

Retrieve articles in all journals with MSC: 65D05, 41A05, 65D07


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0679444-7
Keywords: Bivariate interpolation, scattered data interpolation, random data interpolation, splines, multivariate approximation and interpolation
Article copyright: © Copyright 1983 American Mathematical Society