论文信息 - An Intrinsic Approach to Multivariate Spline Interpolation at Arbitrary Points

An Intrinsic Approach to Multivariate Spline Interpolation at Arbitrary Points

The mathematical theory underlying the practical method of “surface spline interpolation” provides approximation theory with an intrinsic concept of multivariate spline ready for use. A proper abstract setting is shown to be some Hilbert function space, the reproducing kernel of which involves no functions more complicated than logarithms. The crux of the matter is that convenient representation forpiulas can be obtained by resorting to convolutions or to Fourier transforms of distributions.

J. Meinguet

[1] J. Deny,et al. Les espaces du type de Beppo Levi , 1954 .

[2] J. Lions,et al. Sur la complétion par rapport à une intégrale de Dirichlet , 1956 .

[3] M. Agranovich. PARTIAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS , 1961 .

[4] M. Newman,et al. Interpolation and approximation , 1965 .

[5] J. L. Walsh,et al. The theory of splines and their applications , 1969 .

[6] M. Atteia. Fonctions «spline» et noyaux reproduisants d'Aronszajn-Bergman , 1970 .

[7] J. C. Eilbeck. Table errata: Higher transcendental functions. Vol. I, II (McGraw-Hill, New York, 1953) by A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi , 1971 .

[8] Harold S. Shapiro,et al. Topics in Approximation Theory , 1971 .

[9] R. N. Desmarais,et al. Interpolation using surface splines. , 1972 .

[10] K. K. Vo,et al. Distributions, analyse de Fourier, opérateurs aux dérivées partielles , 1972 .

[11] T. J. Rivlin. The Chebyshev polynomials , 1974 .

[12] Jean Duchon,et al. Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces , 1976 .

[13] Jean Duchon,et al. Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[14] J. Meinguet. Multivariate interpolation at arbitrary points made simple , 1979 .