positive lagrange polynomials
نویسندگان
چکیده
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.
منابع مشابه
Stieltjes polynomials and Lagrange interpolation
Bounds are proved for the Stieltjes polynomial En+1, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process...
متن کاملLagrange polynomials of lower sets
A lower set of nodes is a subset of a grid that can be indexed by a lower set of indices. In order to apply the Lagrange interpolation formula, it is convenient to express the Lagrange fundamental polynomials as sums of few terms. We present such a formula for the Lagrange interpolation formula in two variables. In the general multidimensional case, we express the Lagrange fundamental polynomia...
متن کاملBridging Bernstein and Lagrange polynomials
Linear combinations of iterates of Bernstein polynomials exponentially converging to the Lagrange interpolating polynomial are given. The results are applied in CAGD to get an exponentially fast weighted progressive iterative approximation technique to fit data with finer and finer precision. AMS subject classifications: 41A25, 41A36
متن کاملMultivariate Positive Laurent Polynomials
Recently Dritschel proves that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dritschel theorem. Our proof is based on the univariate matrix Féjer-Riesz theorem. Then we discuss a computational method to find approximates of polynomial matrix factorization. Some numerical examples will be shown. F...
متن کاملMatrices of positive polynomials
Associated to a squarematrix all of whose entries are real Laurent polynomials in several variables with no negative coefficients is an ordered “dimension” module introduced by Tuncel, with additional structure, which acts as an invariant for topological Markov chains, and is also an invariant for actions of tori on AF C*-algebras. In describing this invariant, we are led naturally to eventuall...
متن کاملExtremal Positive Trigonometric Polynomials
There are various reasons for the interest in the problem of constructing nonnegative trigonometric polynomials. Among them are: Cesàro means and Gibbs’ phenomenon of the the Fourier series, approximation theory, univalent functions and polynomials, positive Jacobi polynomial sums, orthogonal polynomials on the unit circle, zero-free regions for the Riemann zeta-function, just to mention a few....
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
iranian journal of science and technology (sciences)ISSN 1028-6276
دوره 32
شماره 3 2008
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023