Shepard interpolation is known to produce flat horizontal spots at and around data points. The phenomenon is caused by Shepard’s use of rational inversedistance weight functions, producing similar values around data points. In this paper, a parametric version of Shepard interpolation is introduced that avoids flat horizontal spots. Because Shepard interpolation or its parametric version does no...

Scattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cub...

Two extensions of classical Shepard operators to the fuzzy case are presented. We study Shepard-type interpolation/approximation operators for functions with domain and range in the fuzzy number’s space and max-product approximation operators. Error estimates are obtained in terms of the modulus of continuity.

We show how to combine local Shepard operators with Hermite polynomials on the simplex (Chui and Lai, 1990 [3]) so as to raise the algebraic precision of the Shepard-Taylor operators (Farwig, 1986 [8]) that use the same data and contemporaneously maintain the interpolation properties at each sample point (derivative data included) and a good accuracy of approximation. Numerical results are prov...

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp...