Verified Error Bounds for Linear Systems Through the Lanczos Process

Andreas Frommer () and Andre Weinberg ()
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Andreas Frommer: Bergische Universität Wuppertal, Fachbereich Mathematik
Andre Weinberg: Bergische Universität Wuppertal, Fachbereich Mathematik

A chapter in Developments in Reliable Computing, 1999, pp 255-267 from Springer

Abstract: 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.

Keywords: Quadrature Rule; Interval Arithmetic; Tridiagonal Matrix; Symmetric Positive Definite Matrix; Interval Vector (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-1247-7_20

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DOI: 10.1007/978-94-017-1247-7_20

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