Best Approximation by Linear Superpositions (Approximate Nomography)

Best Approximation by Linear Superpositions (Approximate Nomography)

by S. Ya. Khavinson
     
 

ISBN-10: 0821804227

ISBN-13: 9780821804223

Pub. Date: 11/26/1996

Publisher: American Mathematical Society

This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions $D$ considered as a subspace of the space of continuous functions $C(X)$ on a compact space $X$. Such properties as

Overview

This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions $D$ considered as a subspace of the space of continuous functions $C(X)$ on a compact space $X$. Such properties as density of $D$ in $C(X)$, its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.

Product Details

ISBN-13:
9780821804223
Publisher:
American Mathematical Society
Publication date:
11/26/1996
Series:
Translations of Mathematical Monographs Series, #159
Pages:
175

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >