Multiresolution Data Analysis - Numerical Realization by use of Domain Decomposition Methods and Fast Multipole Techniques / Multiscale Solutions of Oblique Boundary-Value Problems by Layer Potentials
- This survey paper deals with multiresolution analysis from geodetically relevant data and its numerical realization for functions harmonic outside a (Bjerhammar) sphere inside the Earth. Harmonic wavelets are introduced within a suit- able framework of a Sobolev-like Hilbert space. Scaling functions and wavelets are defined by means of convolutions. A pyramid scheme provides efficient implementation und economical computation. Essential tools are the multiplicative Schwarz alternating algorithm (providing domain decomposition procedures) and fast multipole techniques (accelerating iterative solvers of linear systems).