Multivariate Perpendicular Interpolation.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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An approach to multivariate interpolation is described. The algorithm is applicable in arbitrary dimensions, and can generate surfaces of arbitrary smoothness. This is accomplished by tesselating the polyhedral domain into simplices and using one dimensional algorithms to construct interpolants first on edges and then successively on higher order faces by blending methods. The result is a piecewise rational function of a high degree which has the prescribed global smoothness and interpolates to the origninal data. The interpolants are local, i.e. their evaluation at a point requires only data on the simplex that the point resides in. The schemes require data of the same degree as the degree of global smoothness. The degree of polynomial precision is greater than or equal to the degree of smoothness. The approach derives its power and simplicity from the fact that derivatives in directions perpendicularly across faces are incorporated directly as data. Author
- Statistics and Probability