Recurrence Relations for Multivariate B-Splines.

Abstract : We prove recurrence relations for a general class of multivariate B-splines, obtained as 'projections' of convex polyhedra. Our results are simple consequences of Stokes' theorem and include, as special cases, the recurrence relations for the standard multivariate simplicial B-spline. (Author)

[1]  C. D. Boor,et al.  Splines as linear combinations of B-splines. A Survey , 1976 .

[2]  W. Dahmen,et al.  Konstruktion Mehrdimensionaler B-Splines und Ihre Anwendung auf Approximationsprobleme , 1980 .

[3]  Paul Kergin,et al.  A natural interpolation of Ck functions , 1980 .

[4]  Wolfgang Dahmen,et al.  On limits of multivariateB-splines , 1981 .

[5]  C. Micchelli On a numerically efficient method for computing multivariate B-splines , 1979 .

[6]  C. Micchelli,et al.  On the Linear Independence of Multivariate B-Splines. II: Complete Configurations , 1983 .

[7]  Wolfgang Dahmen,et al.  Computation of inner products of multivariate B-splines , 1981 .

[8]  Wolfgang Dahmen,et al.  On Multivariate B-Splines , 1980 .

[9]  Wolfgang Dahmen,et al.  Multivariate B-Splines — Recurrence Relations and Linear Combinations of Truncated Powers , 1979 .

[10]  Charles A Micchelli,et al.  A Constructive Approach to Kergin Interpolation in R(k). , 1978 .

[11]  Klaus Höllig,et al.  B-splines from parallelepipeds , 1982 .

[12]  I. J. Schoenberg,et al.  On Pólya frequency functions IV: The fundamental spline functions and their limits , 1966 .

[13]  Ronald A. DeVore,et al.  Approximation by smooth multivariate splines , 1983 .

[14]  I. J. Schoenberg,et al.  On Pólya frequency functions IV: The fundamental spline functions and their limits , 1966 .

[15]  W. Dahmen APPROXIMATION BY SMOOTH MULTIVARIATE SPLINES ON NON-UNIFORM GRIDS , 1980 .

[16]  S. L. Lee,et al.  Spline approximation operators of Bernstein-Schoenberg type in one and two variables , 1981 .