Transfinite mean value interpolation in general dimension

AbstractMean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative at the boundary; and the construction of a Hermite interpolant when normal derivative data is also available. In this paper we generalize these results to domains in arbitrary dimension

Box-Spline Tilings

We describe a simple method for generating tilings of IR d . The basic tile is defined as# := {x # IR d : |f(x)| < |f(x + j)| #j # ZZ d \0}, with f a real analytic function for which |f(x + j)| # # as |j| # # for almost every x