Ridge Functions

Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.

Allan Pinkus (Author)

9781107124394, Cambridge University Press

Hardback, published 7 August 2015

218 pages, 4 b/w illus.
23.5 x 15.8 x 1.7 cm, 0.45 kg

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.

Preface
Glossary of selected symbols
1. Introduction
2. Smoothness
3. Uniqueness
4. Identifying functions and directions
5. Polynomial ridge functions
6. Density and representation
7. Closure
8. Existence and characterization of best approximations
9. Approximation algorithms
10. Integral representations
11. Interpolation at points
12. Interpolation on lines
References
Supplemental references
Author index
Subject index.

Subject Areas: Maths for computer scientists [UYAM], Calculus & mathematical analysis [PBK], Mathematics [PB]