Polynomial Approximation on Varying Sets

On adaptive local polynomial approximation with varying bandwidth

The local polynomial approximation (LPA) of noisy data is considered with the new adaptive procedure for varying bandwidth selection. The algorithm is simple to implement and nearly optimal within In N factor in the point-wise risk for estimating the function and its derivatives. The adaptive varying bandwidth enables the algorithm to be spatial adaptive over a wide range of the classes of func...

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...

Weighted Approximation on Compact Sets

For a compact set E with connected complement in the com plex plane we consider a problem of the uniform approximation on E by the weighted polynomials W z Pn z where W z is a continuous non vanishing weight function on E analytic in the interior of E Let A E W be the set of functions uniformly approximable on E by such weighted polynomials If E has empty interior then A E W is completely char ...