The aim of this paper is to study the Lagrange multivariate interpolation problems in the space of polynomials of w-degree n. Some new results concerning the polynomial spaces of w-degree n are given. An algorithm for obtaining the w-minimal interpolation space is presented. Key–Words: Lagrange multivariate polynomial interpolation, whomogeneous polynomial spaces, Generalize degree.

Locating good points for multivariate polynomial approximation, in particular interpolation, is an open challenging problem, even in standard domains. One set of points that is always good, in theory, is the so-called Fekete points. They are defined to be those points that maximize the (absolute value of the) Vandermonde determinant on the given compact set. However, these are known analyticall...

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.

This paper presents a new approach for optimizing the non-normalized kurtosis under unit power constraint. It is inspired from the famous FastICA algorithm which uses a fixed-point algorithm and computes fourth-order statistics at each step of the optimization, which is very demanding in terms of both computation time and memory space, especially when the number of samples is high. Our method a...

Sometimes the assumption on the form (1.1) of the solution to the scattered data interpolation Problem 1.2.1 is extended by adding certain polynomials to the expansion,

This study attempts to characterize and predict stock index series in Shenzhen stock market using the concepts of multivariate local polynomial regression. Based on nonlinearity and chaos of the stock index time series, multivariate local polynomial prediction methods and univariate local polynomial prediction method, all of which use the concept of phase space reconstruction according to Taken...

A Abstract n algorithm is presented which reduces the prob-m lem of finding the irreducible factors of a bivariate polyno-ial with integer coefficients in polynomial time in the total i degree and the coefficient lengths to factoring a univariate nteger polynomial. Together with A. Lenstra's, H. Lenstra's u and L. Lovasz' polynomial-time factorization algorithm for nivariate integer polynomials...

In this paper we introduce multivariate hyperedge elimination polynomials and multivariate chromatic polynomials for hypergraphs. The first set of polynomials is defined in terms of a deletion-contraction-extraction recurrence, previously investigated for graphs by Averbouch, Godlin, and Makowsky. The multivariate chromatic polynomial is an equivalent polynomial defined in terms of colorings, a...

We rst review the basic properties of the well known classes of Toeplitz Hankel Vandermonde and other related structured matrices and re examine their correlation to operations with univariate polynomials Then we de ne some natural extensions of such classes of matrices based on their correlation to multivariate polynomials We describe the correlation in terms of the associated operators of mul...