Ridge functions:
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 multivar...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | Cambridge tracts in mathematics
205 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| 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 |
| Physical Description: | 1 Online-Ressource (x, 207 Seiten) |
| ISBN: | 9781316408124 |
| DOI: | 10.1017/CBO9781316408124 |
Staff View
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| 505 | 8 | |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 | |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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Record in the Search Index
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| author | Pinkus, Allan 1946- |
| author_GND | (DE-588)110369297 |
| author_facet | Pinkus, Allan 1946- |
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| bvnumber | BV043940336 |
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| collection | ZDB-20-CBO |
| 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 |
| ctrlnum | (ZDB-20-CBO)CR9781316408124 (OCoLC)930540809 (DE-599)BVBBV043940336 |
| dewey-full | 515/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.73 |
| dewey-search | 515/.73 |
| dewey-sort | 3515 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781316408124 |
| format | Electronic eBook |
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| id | DE-604.BV043940336 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781316408124 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349306 |
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| physical | 1 Online-Ressource (x, 207 Seiten) |
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| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge University Press |
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| series2 | Cambridge tracts in mathematics |
| spelling | Pinkus, Allan 1946- Verfasser (DE-588)110369297 aut Ridge functions Allan Pinkus Cambridge Cambridge University Press 2015 1 Online-Ressource (x, 207 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 205 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 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 Function spaces Multivariate analysis Numbers, Real Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 s Mehrere Variable (DE-588)4277015-4 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-12439-4 https://doi.org/10.1017/CBO9781316408124 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Pinkus, Allan 1946- Ridge functions 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 Function spaces Multivariate analysis Numbers, Real Mehrere Variable (DE-588)4277015-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| subject_GND | (DE-588)4277015-4 (DE-588)4071510-3 |
| title | Ridge functions |
| title_auth | Ridge functions |
| title_exact_search | Ridge functions |
| title_full | Ridge functions Allan Pinkus |
| title_fullStr | Ridge functions Allan Pinkus |
| title_full_unstemmed | Ridge functions Allan Pinkus |
| title_short | Ridge functions |
| title_sort | ridge functions |
| topic | Function spaces Multivariate analysis Numbers, Real Mehrere Variable (DE-588)4277015-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| topic_facet | Function spaces Multivariate analysis Numbers, Real Mehrere Variable Funktion Mathematik |
| url | https://doi.org/10.1017/CBO9781316408124 |
| work_keys_str_mv | AT pinkusallan ridgefunctions |