Dahmen, W. Multiscale methods and wavelets – concepts and applications. (Multiskalen-Methoden and Wavelets – Konzepte und Anwendungen.) (German) Zbl 0835.65126 Jahresber. Dtsch. Math.-Ver. 97, No. 3, 97-114 (1995). The paper gives an overview over applications of multiscale methods in numerical mathematics and sketches further developments in this direction. Especially, it addresses the preconditioning of stiffness matrices arising in the Galerkin solution of elliptic partial differential equations and the compression (preconditioning) of full- populated matrices appearing in the Petrov-Galerkin solution of special integral- and pseudo-differential equations.For details, the author suggests reference to other papers on the same topic, in many cases written by himself and coauthors. Reviewer: G.Steidl (Darmstadt) MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65J10 Numerical solutions to equations with linear operators 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 65F10 Iterative numerical methods for linear systems 65R20 Numerical methods for integral equations 65F35 Numerical computation of matrix norms, conditioning, scaling 35S15 Boundary value problems for PDEs with pseudodifferential operators 35J25 Boundary value problems for second-order elliptic equations 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) 47G30 Pseudodifferential operators 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 47A50 Equations and inequalities involving linear operators, with vector unknowns Keywords:wavelets; matrix compression; Petrov-Galerkin methods; integral equations; survey article; multiscale methods; preconditioning; stiffness matrices; pseudo-differential equations × Cite Format Result Cite Review PDF