Positive sampling in wavelet subspaces
Properties of the hybrid sampling series in wavelet subspaces are studied. The coefficients in such a series are taken to be sampled values of the function to be approximated, which enables one to avoid the integration arising in the ordinary expansion in a scaling function series. The approximations based on this hybrid series have certain desirable convergence properties: they are locally uniformly convergent for locally continuous functions, they have quadratic uniform convergence rate for functions in certain Sobolev spaces, they are locally bounded when the function is locally bounded and therefore, in particular, Gibbs' phenomenon is avoided. Numerical examples are given to illustrate their results and to compare them with the ordinary expansion.
scientific article; zbMATH DE number 1763731