Zur Konvergenz diskreter Least-Squares Methoden auf äquidistanten Stützstellen (English shop)

Preview

Extract, PDF (140 KB)
Table of Contents, PDF (38 KB)

This study examines the method of least squares on an equidistant grid with the aim of approximating a continuous function by a polynomial. More precisely, it investigates for which ratio between the number of nodes and the polynomial degree, and for which functions, the associated operator sequence of the method of least squares converges. This question is studied, using a discrete weight of Jacobi type, with respect to both pointwise and uniform convergence. Accordingly, the relationship between the Jacobi polynomials and the Hahn polynomials is first analysed, and the associated least squares operator is expressed by a truncated series expansion of a function in terms of Hahn polynomials. For the ultraspherical case, new approximation results are obtained under additional assumptions on the functions and on the number of nodes.