Exact constants in approximation theory [EBook] / N. Korneichuk ; translated from the Russian by K. Ivanov.
Exact constants in approximation theory [EBook] / N. Korneichuk ; translated from the Russian by K. Ivanov.
This book is intended as a selfcontained introduction for nonspecialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely rela...
Personal Name(s):  Korneĭchuk, Nikolaĭ Pavlovich, (author) 

Ivanov, K., (translator)  
Imprint: 
Cambridge :
Cambridge University Press,
1990

Physical Description: 
1 online resource (xii, 452 pages) 
Note: 
englisch 
ISBN: 
9780521382342 9780521111560 9781107325791 
Series Title: 
Encyclopedia of mathematics and its applications ;
volume 38 
Subject (LOC):  
Full Text 
This book is intended as a selfcontained introduction for nonspecialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as splineapproximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as selfcontained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with nwidths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists. 