Interpolation and extrapolation optimal designs 1. Polynomial regression and approximation theory (Q2801752)

This book is the first of a series of three which cover a part of the called optimal designs, in the context of interpolation and extrapolation.NEWLINENEWLINEMostly real analysis and approximation of functions is studied here. So it is not surprising that this is examined by tools of statistics. Approximation theory is presented on a very high level including such as the de la Vallée Poussin theorem, the Yakovlevich Remez algorithm.NEWLINENEWLINEThis book is organized in to three parts. In Part 1, the following chapters: Uniform approximation, Convergence rates for the uniform approximation and algorithms, Constrained polynomial approximation, are considered.NEWLINENEWLINEIn Part 2, there are the following chapters: Interpolation and extrapolation designs for the polynomial regression, An introduction and extrapolation problems based on observations on a collection of intervals, Instability of the Lagrange interpolation scheme with respect to measurement errors.NEWLINENEWLINEPart 3 is about Mathematical Materials.NEWLINENEWLINEThe book is excellently organized giving elementary definitions used in the theorem which are explained in well-chosen examples.