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Verified Error Bounds for Linear Systems Through the Lanczos Process

In: Developments in Reliable Computing

Author

Listed:
  • Andreas Frommer

    (Bergische Universität Wuppertal, Fachbereich Mathematik)

  • Andre Weinberg

    (Bergische Universität Wuppertal, Fachbereich Mathematik)

Abstract

We use verified computations and the Lanczos process to obtain guaranteed lower and upper bounds on the 2-norm and the energy-norm error of an approximate solution to a symmetric positive definite linear system. The upper bounds require the a priori knowledge of a lower bound on the smallest eigenvalue.

Suggested Citation

  • Andreas Frommer & Andre Weinberg, 1999. "Verified Error Bounds for Linear Systems Through the Lanczos Process," Springer Books, in: Tibor Csendes (ed.), Developments in Reliable Computing, pages 255-267, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-1247-7_20
    DOI: 10.1007/978-94-017-1247-7_20
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