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

Abstract | References | Similar Articles | Additional Information

Abstract: A method for interpolating scattered data is described. Given , a bivariate function *S* with continuous first order partial derivatives is defined which has the property that . 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.

**[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 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

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