Multiscale, Nonlinear and Adaptive Approximation

Dedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday
2009
ISBN: 978-3-642-03412-1
Verlag: Springer

Buch, Englisch, 660 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1305 g

. 7 7 Hyperbolic partial differential equations and conservation laws. 8 8 Engineering collaborations. 9 9 Thepresent. 9 10 Finalremarks. 10 Publications by Wolfgang Dahmen (as of summer 2009). 10 The way things were in multivariate splines: A personal view. 19 Carl de Boor 1 Tensor product spline interpolation. 19 2 Quasiinterpolation. 20 3 MultivariateB-splines. 21 4 Kergininterpolation.

Zielgruppe

Research

Autoren/Hrsg.

Kunoth, Angela

DeVore, Ronald

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

Introduction: Wolfgang Dahmen’s mathematical work.- The way things were in multivariate splines: A personal view.- On the efficient computation of high-dimensional integrals and the approximation by exponential sums.- Adaptive and anisotropic piecewise polynomial approximation.- Anisotropic function spaces with applications.- Nonlinear approximation and its applications.- Univariate subdivision and multi-scale transforms: The nonlinear case.- Rapid solution of boundary integral equations by wavelet Galerkin schemes.- Learning out of leaders.- Optimized wavelet preconditioning.- Multiresolution schemes for conservation laws.- Theory of adaptive finite element methods: An introduction.- Adaptive wavelet methods for solving operator equations: An overview.- Optimal multilevel methods for (grad), (curl), and (div) systems on graded and unstructured grids.

Über Autor(innen)

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.