Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631705 | Applied Mathematics and Computation | 2010 | 11 Pages |
Abstract
Let Un ⊂ Cn[a, b] be an extended Chebyshev space of dimension n + 1. Suppose that f0 ∈ Un is strictly positive and f1 ∈ Un has the property that f1/f0 is strictly increasing. We search for conditions ensuring the existence of points t0, …, tn ∈ [a, b] and positive coefficients α0, …, αn such that for all f ∈ C[a, b], the operator Bn:C[a, b] → Un defined by Bnf=∑k=0nf(tk)αkpn,k satisfies Bnf0 = f0 and Bnf1 = f1. Here it is assumed that pn,k, k = 0, …, n, is a Bernstein basis, defined by the property that each pn,k has a zero of order k at a and a zero of order n − k at b.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
J.M. Aldaz, O. Kounchev, H. Render,