Multivariate Approximation by V Temlyakov
This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.-
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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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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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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Greedy 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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Algebraic Geometry and Statistical Learning Theory
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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
'This excellent book covers a variety of topics in univariate and multivariate approximation as well as their connection to computational mathematics The exposition is designed in such a way that the reader is familiarized with the univariate results rst and then the transition to the multivariate case is performed, highlighting the challenges and the new methodsThe book is self-contained and is accessible to readers with graduate and advanced undergraduate background.' Andriy V. Prymak, MathSciNet
V. Temlyakov is Carolina Distinguished Professor in the Department of Mathematics at the University of South Carolina. He has written several books on approximation theory, and has received numerous honours and awards. His research interests include greedy approximation, compressed sensing, learning theory and numerical integration.
| SKU | Unavailable |
| ISBN 13 | 9781108428750 |
| ISBN 10 | 1108428754 |
| Title | Multivariate Approximation |
| Author | V Temlyakov |
| Series | Cambridge Monographs On Applied And Computational Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2018-07-19 |
| Number of pages | 550 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |