Polynomial interpolation on the unit ball of R d has a unique solution if the points are located on several spheres inside the ball and the points on each sphere solves the corresponding interpolation problem on the sphere. Furthermore, the solution can be computed in a recursive way.

This paper investigates polynomial interpolation with respect to a nite set of appropriate linear functionals and the close relations to the Grr obner basis of the associated nite dimensional ideal.

Simple proofs are provided for two properties of a new multivariate polynomial interpolation scheme, due to Amos Ron and the author, and a formula for the interpolation error is derived and discussed.

in this research, the spatial distribution of fe, cu, zn and mn on agricultural lands of golestan province were evaluated using different interpolation methods such as, kriging, inverse distance weighted, local polynomial, inverse multiquadric and radial basis function. thus, 505 soil samples were provided from fields during 2008 and micronutrients rates were measured for each sample. the perfo...

In this paper, we propose new deterministic interpolation algorithms and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let f be an n-variate polynomial with a degree bound D and and term bound T . Our deterministic algorithms have better complexities than existing deterministic interpolation algorithms in most cases. Our Monte Ca...

As known, the problem of choosing ‘‘good’’ nodes is a central one in polynomial interpolation. While the problem is essentially solved in one dimension (all good nodal sequences are asymptotically equidistributed with respect to the arc-cosine metric), in several variables it still represents a substantially open question. In this work we consider new nodal sets for bivariate polynomial interpo...

Based on a generalized algorithm for the division with remainder of polynomials in several variables, a method for the construction of standard bases for polynomial ideals with respect to arbitrary grading structures is derived. In the case of ideals with finite codimension, which can be viewed upon as a polynomial interpolation problem, an explicit representation for the interpolation space of...

In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...

In this paper, we provide an integral error formula for a certain scale of mean value interpolations which includes the multivariate polynomial interpolation schemes of Kergin and Hakopian. This formula involves only derivatives of order one higher than the degree of the interpolating polynomial space, and from it we can obtain sharp L∞-estimates. These L∞-estimates are precisely those that num...