POSITIVE LAGRANGE POLYNOMIALS

Abstract

In this paper we demonstrate the existence of a set of polynomials Pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in theLagrange interpolation process. In other words, if a  a1  an  b is a given finite sequence of realnumbers, then Pi (a j )  ij (ij is the Kronecker delta symbol ) ; moreover, the sum of Pi 's is identically 1.