Nonlinear Approximation Theory by Dietrich Braess
The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approxima- tion is strongly connected with his name. By making use of his ideas, the theories of best uniform approximation by rational functions and by polynomials were developed over the years in an almost unified framework. The difference between linear and rational approximation and its implications first became apparent in the 1960's. At roughly the same time other approaches to nonlinear approximation were also developed. The use of new tools, such as nonlinear functional analysis and topological methods, showed that linearization is not sufficient for a complete treatment of nonlinear families. In particular, the application of global analysis and the consideration of flows on the family of approximating functions intro- duced ideas which were previously unknown in approximation theory. These were and still are important in many branches of analysis. On the other hand, methods developed for nonlinear approximation prob- lems can often be successfully applied to problems which belong to or arise from linear approximation. An important example is the solution of moment problems via rational approximation. Best quadrature formulae or the search for best linear spaces often leads to the consideration of spline functions with free nodes. The most famous problem of this kind, namely best interpolation by poly- nomials, is treated in the appendix of this book.-
Numerical Analysis for Elliptic Optimal Control Problems
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Introduction to Shape Optimization
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Numerical Methods for Two-phase Incompressible Flows
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Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
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Spectral Methods
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The Graduate Student's Guide to Numerical Analysis '98
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The Linearization Method for Constrained Optimization
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Hilbert Space Splittings and Iterative Methods
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The Concept of Stability in Numerical Mathematics
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Monotone Discretizations for Elliptic Second Order Partial Differential Equations
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Boundary Element Methods
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History of Continued Fractions and Padé Approximants
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Method of Difference Potentials and Its Applications
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Newton Methods for Nonlinear Problems
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High Order Difference Methods for Time Dependent PDE
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Logarithmic Norms
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Minimization Methods for Non-Differentiable Functions
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Numerical Toolbox for Verified Computing I
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Hierarchical Matrices: Algorithms and Analysis
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Mixed and Hybrid Finite Element Methods
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Solving Elliptic Problems Using ELLPACK
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Discrete Iterations
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Numerical Techniques for Stochastic Optimization
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Numerical Continuation Methods
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Krylov Methods for Nonsymmetric Linear Systems
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Progress in Approximation Theory
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Sequence Transformations
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Moduli of Smoothness
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Numerical Methods Based on Sinc and Analytic Functions
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Krylov Subspace Methods for Linear Systems
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Advanced Boundary Element Methods
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Retarded Potentials and Time Domain Boundary Integral Equations
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Numerical Modeling in Materials Science and Engineering
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Robust Numerical Methods for Singularly Perturbed Differential Equations
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Finite Element Methods for Incompressible Flow Problems
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Solving Ordinary Differential Equations I
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Solving Ordinary Differential Equations II
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Tensor Spaces and Numerical Tensor Calculus
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Matrix Iterative Analysis
Braess, Dietrich: - Dietrich Braess is Professor of Mathematics at Ruhr University Bochum, Germany.
| SKU | Unavailable |
| ISBN 13 | 9783642648830 |
| ISBN 10 | 3642648835 |
| Title | Nonlinear Approximation Theory |
| Author | Dietrich Braess |
| Series | Springer Series In Computational Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2011-10-01 |
| Number of pages | 290 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |