Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of his 60th BirthdayRonald DeVore, Angela Kunoth The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building the foundation for most efficient numerical algorithms for simulating complex phenomena. |
Contents
| 1 | |
| 19 | |
On the efficient computation of highdimensional integrals and the approximation by exponential sums | 39 |
Adaptive and anisotropic piecewise polynomial approximation | 75 |
Anisotropic function spaces with applications | 137 |
Nonlinear approximation and its applications | 169 |
The nonlinear case | 203 |
Rapid solution of boundary integral equations by wavelet Galerkin schemes | 249 |
Learning out of leaders | 295 |
Optimized wavelet preconditioning | 325 |
Multiresolution schemes for conservation laws | 379 |
An introduction | 409 |
An overview | 543 |
Optimal multilevel methods for Hgrad Hcurl and Hdiv systems on graded and unstructured grids | 599 |
Other editions - View all
Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang ... Ronald DeVore,Angela Kunoth No preview available - 2014 |
Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang ... Ronald DeVore,Angela Kunoth No preview available - 2010 |
Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang ... Ronald DeVore,Angela Kunoth No preview available - 2009 |
Common terms and phrases
adaptive wavelet AFEM Anal analysis anisotropic applied asymptotic B-splines basis Besov spaces bilinear form biorthogonal bisection bounded box splines C.A. Micchelli coefficients compression computation construction convergence rate convex corresponding curve Dahmen decomposition defined denote derived DeVore discrete domain edge ellipsoid cover elliptic equivalent error estimate exists exponential exponential sums finite element method finite element spaces Galerkin given greedy greedy algorithms grid Hilbert space implies inequality interpolation iteration Lemma linear Lp norm Math matrix mesh multilevel multiresolution multiscale multivariate nodes nonlinear norm numerical obtain optimal parameter partitions PDEs piecewise constant piecewise polynomial polygonal preconditioner problem proof properties Riesz Riesz basis saddle point satisfies Sect Section sequence SIAM smax smooth Sobolev spaces solution spline stability subdivision schemes subspace tensor product Theorem theory tion triangulation vector vertex wavelet bases wavelet methods