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Greedy Approximation.
Provides the theoretical foundations for algorithms widely used in numerical mathematics. Includes classical results, as well as the latest advances.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2011.
|
| Colección: | Cambridge monographs on applied and computational mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Temlyakov, Vladimir. | |
| 245 | 1 | 0 | |a Greedy Approximation. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (434 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge Monographs on Applied and Computational Mathematics ; |v v. 20 | |
| 505 | 0 | |a Cover; CAMBRIDGE MONOGRAPHS ON APPLIED AND COMPUTATIONAL MATHEMATICS; 20 Greedy Approximation; Title; Copyright; Contents; Preface; 1 Greedy approximation with regard to bases; 1.1 Introduction; 1.2 Schauder bases in Banach spaces; 1.3 Greedy bases; 1.4 Quasi-greedy and almost greedy bases; 1.5 Weak Greedy Algorithms with respect to bases; 1.6 Thresholding and minimal systems; 1.7 Greedy approximation with respect to the trigonometric system; 1.8 Greedy-type bases; direct and inverse theorems; 1.9 Some further results; 1.10 Systems Lp-equivalent to the Haar basis; 1.11 Open problems. | |
| 505 | 8 | |a 2 Greedy approximation with respect to dictionaries: Hilbert spaces2.1 Introduction; 2.2 Convergence; 2.3 Rate of convergence; 2.3.1 Upper bounds for approximation by general dictionaries; 2.3.2 Upper estimates for weak-type greedy algorithms; 2.4 Greedy algorithms for systems that are not dictionaries; 2.5 Greedy approximation with respect to?-quasi-orthogonal dictionaries; 2.6 Lebesgue-type inequalities for greedy approximation; 2.6.1 Introduction; 2.6.2 Proofs; 2.7 Saturation property of greedy-type algorithms; 2.7.1 Saturation of the Pure Greedy Algorithm. | |
| 505 | 8 | |a 2.7.2 A generalization of the Pure Greedy Algorithm2.7.3 Performance of the n-Greedy Algorithm with regard to an incoherent dictionary; 2.8 Some further remarks; 2.9 Open problems; 3 Entropy; 3.1 Introduction: definitions and some simple properties; 3.2 Finite dimensional spaces; 3.3 Trigonometric polynomials and volume estimates; 3.3.1 Univariate trigonometric polynomials; 3.3.2 Multivariate trigonometric polynomials; The Dirichlet kernels.; The Fejér kernels.; The de la Vallée Poussin kernels.; The Rudin-Shapiro polynomials.; 3.3.3 Volume estimates; generalized Rudin-Shapiro polynomials. | |
| 505 | 8 | |a 3.4 The function classes3.5 General inequalities; 3.6 Some further remarks; 3.7 Open problems; 4 Approximation in learning theory; 4.1 Introduction; 4.1.1 Approximation theory; recovery of functions; 4.1.2 Statistics; regression theory; 4.1.3 Learning theory; 4.2 Some basic concepts of probability theory; 4.2.1 The measure theory and integration; 4.2.2 The concentration of measure inequalities; 4.2.3 The Kullback-Leibler information and the Hellinger distance; 4.3 Improper function learning; upper estimates; 4.3.1 Introduction; 4.3.2 First estimates for classes from Sr. | |
| 505 | 8 | |a 4.3.3 Further estimates for classes from Sr chaining technique; 4.3.4 Least squares estimators for convex hypothesis spaces; 4.3.5 Least squares estimators for non-convex hypothesis spaces; 4.3.6 Estimates for classes from Sr2; 4.3.7 Estimates for classes from Sr1; 4.4 Proper function learning; upper estimates; 4.4.1 Introduction; 4.4.2 The least squares estimators; 4.4.3 Some examples; 4.5 The lower estimates; 4.5.1 Introduction; 4.5.2 The projection learning; 4.5.3 Lower estimates for the Bernoulli scheme; 4.5.4 The proper function learning. | |
| 500 | |a 4.6 Application of greedy algorithms in learning theory. | ||
| 520 | |a Provides the theoretical foundations for algorithms widely used in numerical mathematics. Includes classical results, as well as the latest advances. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Approximation theory. | |
| 650 | 6 | |a Théorie de l'approximation. | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 0 | 7 | |a Aproximación, Teoría de |2 embucm |
| 650 | 7 | |a Approximation theory |2 fast | |
| 650 | 7 | |a Greedy-Algorithmus |2 gnd | |
| 650 | 7 | |a Approximationsalgorithmus |2 gnd | |
| 650 | 7 | |a Nichtlineare Approximation |2 gnd | |
| 758 | |i has work: |a Greedy approximation (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGyBtdc9rMMJqbWMC3bDMd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Temlyakov, Vladimir. |t Greedy Approximation. |d Cambridge : Cambridge University Press, ©2011 |z 9781107003378 |
| 830 | 0 | |a Cambridge monographs on applied and computational mathematics. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=807191 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- CAMBRIDGE MONOGRAPHS ON APPLIED AND COMPUTATIONAL MATHEMATICS -- 20 Greedy Approximation -- Title -- Copyright -- Contents -- Preface -- 1 Greedy approximation with regard to bases -- 1.1 Introduction -- 1.2 Schauder bases in Banach spaces -- 1.3 Greedy bases -- 1.4 Quasi-greedy and almost greedy bases -- 1.5 Weak Greedy Algorithms with respect to bases -- 1.6 Thresholding and minimal systems -- 1.7 Greedy approximation with respect to the trigonometric system -- 1.8 Greedy-type bases -- direct and inverse theorems -- 1.9 Some further results -- 1.10 Systems Lp-equivalent to the Haar basis -- 1.11 Open problems -- 2 Greedy approximation with respect to dictionaries: Hilbert spaces -- 2.1 Introduction -- 2.2 Convergence -- 2.3 Rate of convergence -- 2.3.1 Upper bounds for approximation by general dictionaries -- 2.3.2 Upper estimates for weak-type greedy algorithms -- 2.4 Greedy algorithms for systems that are not dictionaries -- 2.5 Greedy approximation with respect to λ-quasi-orthogonal dictionaries -- 2.6 Lebesgue-type inequalities for greedy approximation -- 2.6.1 Introduction -- 2.6.2 Proofs -- 2.7 Saturation property of greedy-type algorithms -- 2.7.1 Saturation of the Pure Greedy Algorithm -- 2.7.2 A generalization of the Pure Greedy Algorithm -- 2.7.3 Performance of the n-Greedy Algorithm with regard to an incoherent dictionary -- 2.8 Some further remarks -- 2.9 Open problems -- 3 Entropy -- 3.1 Introduction: definitions and some simple properties -- 3.2 Finite dimensional spaces -- 3.3 Trigonometric polynomials and volume estimates -- 3.3.1 Univariate trigonometric polynomials -- 3.3.2 Multivariate trigonometric polynomials -- The Dirichlet kernels. -- The Fejér kernels. -- The de la Vallée Poussin kernels. -- The Rudin-Shapiro polynomials. -- 3.3.3 Volume estimates -- generalized Rudin-Shapiro polynomials. | |
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