Discrete orthogonal polynomials on Gauss–Lobatto Chebyshev nodes

Discrete orthogonal polynomials on Gauss-Lobatto Chebyshev nodes

In this paper we present explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev points. We also give the “three-term recurrence relation” to construct such polynomials. As a numerical application, we apply our formulas to the least-squares problem.

Bivariate Chebyshev-i Weighted Orthogonal Polynomials on Simplicial Domains

We construct a simple closed-form representation of degree-ordered system of bivariate Chebyshev-I orthogonal polynomials Tn,r(u, v, w) on simplicial domains. We show that these polynomials Tn,r(u, v, w), r = 0, 1, . . . , n; n ≥ 0 form an orthogonal system with respect to the Chebyshev-I weight function.

On Discrete Orthogonal Polynomials of Several Variables

Let V be a set of points in R. Define a linear functional L on the space of polynomials, Lf = ∑ x∈V f(x)ρ(x), where ρ is a nonzero function on V . The structure of discrete orthogonal polynomials of several variables with respect to the bilinear form 〈f, g〉 = L(fg) is studied. For a given V , the subspace of polynomials that will generate orthogonal polynomials on V is identified. One result sh...

On Generating Orthogonal Polynomials for Discrete Measures

Global asymptotics of the discrete Chebyshev polynomials

In this paper, we study the asymptotics of the discrete Chebyshev polynomials tn(z,N) as the degree grows to infinity. Global asymptotic formulas are obtained as n → ∞, when the ratio of the parameters n/N = c is a constant in the interval (0, 1). Our method is based on a modified version of the Riemann-Hilbert approach first introduced by Deift and Zhou.