$${\mathcal{H}}^{2}$$ -Matrix Compression View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2012

AUTHORS

Steffen Börm

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. More... »

PAGES

339-362

References to SciGraph publications

  • 2005-08. Hybrid cross approximation of integral operators in NUMERISCHE MATHEMATIK
  • 2006-02. -Matrix Arithmetics in Linear Complexity in COMPUTING
  • 2010-04. Approximation of solution operators of elliptic partial differential equations by - and -matrices in NUMERISCHE MATHEMATIK
  • 2003-04. Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices in COMPUTING
  • 2000-02. A Sparse ℋ-Matrix Arithmetic. in COMPUTING
  • 2000-10. Approximation of boundary element matrices in NUMERISCHE MATHEMATIK
  • 2004-06. Low-Rank Approximation of Integral Operators by Interpolation in COMPUTING
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  • 1999-04. A Sparse Matrix Arithmetic Based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Cal H$\end{document}-Matrices. Part I: Introduction to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Cal H}$\end{document}-Matrices in COMPUTING
  • 2003-07. Existence of ℋ-matrix approximants to the inverse FE-matrix of elliptic operators with L∞-coefficients in NUMERISCHE MATHEMATIK
  • 2009-06. Domain decomposition based -LU preconditioning in NUMERISCHE MATHEMATIK
  • Book

    TITLE

    New Developments in the Visualization and Processing of Tensor Fields

    ISBN

    978-3-642-27342-1
    978-3-642-27343-8

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-27343-8_18

    DOI

    http://dx.doi.org/10.1007/978-3-642-27343-8_18

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1011352634


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