Ridge functions / Allan Pinkus.

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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...

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Bibliographic Details
Main Author: Pinkus, Allan, 1946- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2015.
Series:Cambridge tracts in mathematics ; 205.
Subjects:
Function spaces.
Multivariate analysis.
Numbers, Real.
Physical Description:x, 207 pages : illustrations ; 24 cm.
Format: Book

MARC

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300 |a x, 207 pages :  |b illustrations ;  |c 24 cm. 
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504 |a Includes bibliographical references (pages 196-201) and index. 
505 0 |a 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. 
520 3 |a 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. 
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