Greedy Approximation by Vladimir Temlyakov
This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.-
Algebraic Geometry and Statistical Learning Theory
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Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
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Kernel-Based Methods
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Infinite-Dimensional Spectral Computations
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Numerical Bifurcation Analysis of Maps
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Collocation Methods for Volterra Integral and Related Functional Differential Equations
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The Mathematical Foundations of Mixing
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Partial Differential Equation Methods for Image Inpainting
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Topology for Computing
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High-Order Methods for Incompressible Fluid Flow
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Generalized Riemann Problems in Computational Fluid Dynamics
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Multivariate Approximation
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Iterative Krylov Methods for Large Linear Systems
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Dynamical Systems and Numerical Analysis
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Volterra Integral Equations
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Scattered Data Approximation
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A Practical Guide to the Invariant Calculus
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Orthogonal Rational Functions
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Geometry and Topology for Mesh Generation
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Curve and Surface Reconstruction
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The Numerical Solution of Integral Equations of the Second Kind
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Radial Basis Functions
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A Practical Guide to Pseudospectral Methods
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Spectral Methods for Time-Dependent Problems
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Multiscale Methods for Fredholm Integral Equations
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Differential Equations and Variational Methods on Graphs
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Minimal Cubature Rules
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High-Accuracy Finite Difference Methods
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An Introduction to Immersed Boundary Methods
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Modern Computer Arithmetic
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Matrix Preconditioning Techniques and Applications
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Geometry of the Phase Retrieval Problem
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Quasi-Interpolation
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The Christoffel–Darboux Kernel for Data Analysis
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Difference Equations by Differential Equation Methods
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Learning Theory
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Schwarz-Christoffel Mapping
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Simulating Hamiltonian Dynamics
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Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations
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Discrete Variational Problems with Interfaces
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Spaces of Measures and their Applications to Structured Population Models
'The author is the leading expert on greedy approximation and this book offers a guided tour through the state of the art of the subjectTemlyakov's book is an excellent mathematical monograph and a valuable reference for researchers not only in approximation theory, but also in numerical mathematics, analysis, functional analysis, and statistics. The book is addressed mainly to researchers interested in greedy approximation and related areas. However, it is written at a level that is approachable for graduate students interested in the aforementioned areas, and it could be used for designing graduate courses in greedy approximation, learning theory and compressed sensing. As an added bonus, the author has included an extensive list of open problems in the area that can serve as inspiration for future research papers and dissertations.' Morten Nielsen, SIAM News
Vladimir Temlyakov is Carolina Distinguished Professor in the Department of Mathematics at the University of South Carolina.
| SKU | Unavailable |
| ISBN 13 | 9781107003378 |
| ISBN 10 | 1107003377 |
| Title | Greedy Approximation |
| Author | Vladimir Temlyakov |
| Series | Cambridge Monographs On Applied And Computational Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2011-09-08 |
| Number of pages | 432 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |