POSITIVE LAGRANGE POLYNOMIALS

Document Type : Regular Paper

Authors

Department of Mathematics, School of Science, Shiraz University, Shiraz, I. R. of Iran

Abstract

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

Keywords

Iranian Journal of Science
Volume 32, Issue 3 - Serial Number 3
September and October 2008
Pages 191-195

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