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Multiresolution Data Analysis — Numerical Realization by Use of Domain Decomposition Methods and Fast Multipole Techniques

  • Willi Freeden
  • Carsten Mayer
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)

Abstract

This survey paper deals with multiresolution analysis of geodetically relevant data and its numerical realization for functions harmonic outside a (Bjerhammar) sphere inside the Earth. Harmonic wavelets are introduced within a suitable framework of a Sobolev-like Hilbert space. Scaling functions and wavelets are defined by means of convolutions. A pyramid scheme provides efficient implementation and economical computation. Essential tools are the multiplicative Schwarz alternating algorithm (providing domain decomposition procedures) and fast multipole techniques (accelerating iterative solvers of linear systems).

Keywords

Multiresolution analysis harmonic wavelets reconstruction formula pyramid schemes domain decomposition methods fast multipole techniques. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Willi Freeden
    • 1
  • Carsten Mayer
    • 1
  1. 1.Geomathematics Group, Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany

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