By Julian Lowell Coolidge

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NorthHolland, 1983, 135-146. 10. , Elliptic Problems in Nonsmooth Domains, Pitman, 1985. 11. , These de 3^ cycle, Grenoble, 1987. 12. Laurent, P. , Approximation et Optimisation, Hermann, Paris, 1972. 13. Laurent, P. , Inf-convolution spline pour Γ approximation de données discontinues, RAIRO 20 (1986), 89-111. 14. , These d'état, Rennes, 1984. 15. C. and D. Apprato, Estimations de I'erreur d'approximation sur un domaine borne de IR^ par -splines d'interpolation et d'ajustement discretes, Numer.

The rational tetrahedral scheme [2] could not be modified to obtain a scheme. The key idea in [7] is to incorporate perpendicular cross-boundary deriva tives directly. Let S be the simplex in question, and let F be a facet of S. We think of all faces of S as embedded in low dimensional affine subspaces, so that any fine can intersect a face even though the fine may not intersect the simplex S itself. The anchor of F is that facet other than F that forms the smallest angle with F. With a point χ and the facet F we associate the straight line through χ perpendicular to F.

33:^ Dongarra, J. , and E. Grosse, Distribution of mathematical software via electronic mail, Numerical Analysis Manuscript 85-2, AT&T Bell Labora tories, Murray Hill, New Jersey 07974. 34. O. Analyse Numeriques 10 (1976), 5-12. , Interpolation of scattered data by radial functions, in [31], 47-61. 36. Farin, G. ) Geometric Modeling: Algorithms and New Trends, SIAM PubHcations, Philadelphia, 1987. 37. , Rate of convergence of Shepard's global interpolation formula. Math. Comp. 46 (1986), 577-590.