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).
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Freeden, W., Mayer, C. (2004). Multiresolution Data Analysis — Numerical Realization by Use of Domain Decomposition Methods and Fast Multipole Techniques. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_8
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DOI: https://doi.org/10.1007/978-3-662-10735-5_8
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