On polynomial approximation in $A_{q}(D)$

Lectures on multivariate polynomial approximation

Remarks on Piecewise Polynomial Approximation

The theoretical and experimental background for the approximation of "real-world" functions is reviewed to motivate the use of piecewise polynomial approximations. It is possible in practice ~o achieve the results suggested by the theory for piecewise polynomials. A convergent adaptive algorithm is outlined which effectively and efficiently computes smooth piecewise polynomial approxImations to...

Polynomial Approximation

Polynomials are very simple mathematical functions which have the flexibility to represent very general nonlinear relationships. Approximation of more complicated functions by polynomials is a basic building block for many numerical techniques. This article considers two distinct but related applications. The first is polynomial regression in which polynomials are used to model a nonlinear rela...

Trivariate polynomial approximation on Lissajous curves ∗

We study Lissajous curves in the 3-cube that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications co...

Weighted Polynomial Approximation on the Integers

We prove here some polynomial approximation theorems, somewhat related to the Szasz-Mfintz theorem, but where the domain of approximation is the integers, by dualizing a gap theorem of C. l ~ Y I for periodic entire functions. In another Paper [7], we shall prove, by similar means, a completeness theorem ibr some special sets of entire functions. I t is well known (see, for example [l]) tha t i...