Best approximation by linear superpositions (Approximate nomography)

✍ Scribed by S. Ya. Khavinson

• Publisher: American Mathematical Society
• Year: 1996
• Tongue: English, Russian
• Leaves: 182
• Series: Translations of mathematical monographs 159
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content: Discussing Kolmogorov's theorem Approximation of functions of two variables by sums $\varphi (X) + \psi (y)$ Problems of approximation by linear superpositions References.

✦ Subjects

Approximation theory;Functions of several real variables;Functional analysis;Approximation theory;Functional analysis;Functions of several real variables