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Validated Solution of Large Linear Systems

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Validation Numerics

Part of the book series: Computing Supplementum ((COMPUTING,volume 9))

Abstract

Validated Solution of Large Linear Systems. Some new methods will be presented for computing verified inclusions of the solution of large linear systems. The matrix of the linear system is typically of sparse or band structure. There are no prerequisites for the matrix, such as being M-matrix, Symmetric, positive definite or diagonally dominant. For general band matrices of lower, Upper bandwidth p, q of dimension n the Computing time is n · (pq + p 2 + q 2). Examples with up to 1.000.000 unknowns will be presented.

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Author information

Authors and Affiliations

  1. Technische Informatik III, TU Hamburg-Harburg, Eissendorferstrasse 38, D-W-2100, Hamburg 90, Federal Republic of Germany

    Siegfried M. Rump

Authors
  1. Siegfried M. Rump
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Innsbruck, Austria

    R. Albrecht

  2. Institut für Angewandte Mathematik, Universität Karlsruhe, Federal Republic of Germany

    G. Alefeld

  3. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Austria

    H. J. Stetter

Additional information

Dedicated to Professor U. Kulisch on the occasion of his 60th birthday

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© 1993 Springer-Verlag

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Rump, S.M. (1993). Validated Solution of Large Linear Systems. In: Albrecht, R., Alefeld, G., Stetter, H.J. (eds) Validation Numerics. Computing Supplementum, vol 9. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6918-6_15

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  • DOI: https://doi.org/10.1007/978-3-7091-6918-6_15

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82451-1

  • Online ISBN: 978-3-7091-6918-6

  • eBook Packages: Springer Book Archive

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