Ridge functions / Allan Pinkus.

Format:

Book

Author/Creator:

Pinkus, Allan, 1946- author.

Series:

Cambridge tracts in mathematics ; 205.

Cambridge tracts in mathematics ; 205

Language:

English

Subjects (All):

Function spaces.

Multivariate analysis.

Numbers, Real.

Physical Description:

1 online resource (x, 207 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2015.

Summary:

Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field.

Contents:

Introduction

Smoothness

Uniqueness

Indentifying functions and directions

Polynomial ridge functions

Density and representation

Closure

Existence and characterization of best approximations

Approximation algorithms

Integral representations

Interpolation at points

Interpolation on lines.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-316-43045-6

1-316-43471-0

1-316-43542-3

1-316-43826-0

1-316-43968-2

1-316-40812-4

1-316-43613-6

1-316-43684-5