Multiscale, Nonlinear and Adaptive Approximation : Dedicated to Wolfgang Dahmen on the Occasion of His 60th Birthday

Ronald DeVore's speciality is Nonlinear Approximation Theory. He is The Walter E. Koss Professor of Mathematics at Texas A&M University.He was elected a member of the American Academy of Arts and Sciences in 2001 and received an Honorary Doctorate from RWTH Aachen in 2004. In 2006, he was a Plenary Lecturer at the International Congress of Mathematicians in Madrid. Angela Kunoth is working on wavelet and multiscale methods for solving partial differential equations and for data analysis purposes. She holds the Chair of Complex Systems at Universitaet Paderborn since 2007 and is an editor of five journals in applied mathematics and numerics. Front Matter....Pages I-XXIII Introduction: Wolfgang Dahmen’s mathematical work....Pages 1-17 The way things were in multivariate splines: A personal view....Pages 19-37 On the efficient computation of high-dimensional integrals and the approximation by exponential sums....Pages 39-74 Adaptive and anisotropic piecewise polynomial approximation....Pages 75-135 Anisotropic function spaces with applications....Pages 137-167 Nonlinear approximation and its applications....Pages 169-201 Univariate subdivision and multi-scale transforms: The nonlinear case....Pages 203-247 Rapid solution of boundary integral equations by wavelet Galerkin schemes....Pages 249-294 Learning out of leaders....Pages 295-324 Optimized wavelet preconditioning....Pages 325-378 Multiresolution schemes for conservation laws....Pages 379-408 Theory of adaptive finite element methods: An introduction....Pages 409-542 Adaptive wavelet methods for solving operator equations: An overview....Pages 543-597 Optimal multilevel methods for H (grad), H (curl), and H (div) systems on graded and unstructured grids....Pages 599-659 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 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 t