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\({\mathcal{H}}^{2}\)-Matrix Compression

  • Steffen BörmEmail author
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Representing a matrix in a hierarchical data structure instead of the standard two-dimensional array can offer significant advantages: submatrices can be compressed efficiently, different resolutions of a matrix can be handled easily, and even matrix operations like multiplication, factorization or inversion can be performed in the compressed representation, thus saving computation time and storage. \({\mathcal{H}}^{2}\)-matrices use a subdivision of the matrix into a hierarchy of submatrices in combination with a hierarchical basis, similar to a wavelet basis, to handle \(n \times n\) matrices in \(\mathcal{O}(nk)\) units of storage, where k is a parameter controlling the compression error. This chapters gives a short introduction into the basic concepts of the \({\mathcal{H}}^{2}\)-matrix method, particularly concerning the compression of arbitrary matrices.

Notes

Acknowledgements

Most of the research results described in this chapter are the result of several years of work as a researcher at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, and I particularly owe a debt of gratitude to Wolfgang Hackbusch and Lars Grasedyck for many insightful discussions.

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Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Computer ScienceChristian-Albrechts-Universität zu KielKielGermany

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