Greedy approximation /
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Author / Creator: | Temlyakov, Vladimir, 1953- |
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Imprint: | Cambridge ; New York : Cambridge University Press, 2011. |
Description: | xiv, 418 p. : ill. ; 24 cm. |
Language: | English |
Series: | Cambridge monographs on applied and computational mathematics ; 20 Cambridge monographs on applied and computational mathematics ; 20. |
Subject: | |
Format: | Print Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8518415 |
Table of 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 L p -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
- 2.4. 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
- 2.7. Saturation property of greedy-type algorithms
- 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
- 3.4. The function classes
- 3.5. General inequalities
- 3.6. Some further remarks
- 3.7. Open problems
- 4. Approximation in learning theory
- 4.1. Introduction
- 4.2. Some basic concepts of probability theory
- 4.3. Improper function learning; upper estimates
- 4.4. Proper function learning; upper estimates
- 4.5. The lower estimates
- 4.6. Application of greedy algorithms in learning theory
- 5. Approximation in compressed sensing
- 5.1. Introduction
- 5.2. Equivalence of three approximation properties of the compressed sensing matrix
- 5.3. Construction of a good matrix
- 5.4. Dealing with noisy data
- 5.5. First results on exact recovery of sparse signals; the Orthogonal Greedy Algorithm
- 5.6. Exact recovery of sparse signals; the Subspace Pursuit Algorithm
- 5.7. On the size of incoherent systems
- 5.8. Restricted Isometry Property for random matrices
- 5.9. Some further remarks
- 5.10. Open problems
- 6. Greedy approximation with respect to dictionaries: Banach spaces
- 6.1. Introduction
- 6.2. The Weak Chebyshev Greedy Algorithm
- 6.3. Relaxation; co-convex approximation
- 6.4. Free relaxation
- 6.5. Fixed relaxation
- 6.6. Thresholding algorithms
- 6.7. Greedy expansions
- 6.8. Relaxation; X-greedy algorithms
- 6.9. Incoherent dictionaries and exact recovery
- 6.10. Greedy algorithms with approximate evaluations and restricted search
- 6.11. An application of greedy algorithms for the discrepancy estimates
- 6.12. Open problems
- References
- Index