BIT Numerical Mathematics

, Volume 40, Issue 3, pp 471–496 | Cite as

Error Analysis of the Symplectic Lanczos Method for the Symplectic Eigenvalue Problem

  • Heike Fassbender


A rounding error analysis of the symplectic Lanczos algorithm for the symplectic eigenvalue problem is given. It is applicable when no break down occurs and shows that the restriction of preserving the symplectic structure does not destroy the characteristic feature of nonsymmetric Lanczos processes. An analog of Paige's theory on the relationship between the loss of orthogonality among the Lanczos vectors and the convergence of Ritz values in the symmetric Lanczos algorithm is discussed. As to be expected, it follows that (under certain assumptions) the computed J-orthogonal Lanczos vectors loose J-orthogonality when some Ritz values begin to converge.

Symplectic Lanczos method symplectic matrix eigenvalues error analysis 


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© Swets & Zeitlinger 2000

Authors and Affiliations

  • Heike Fassbender
    • 1
  1. 1.Zentrum MathematikTechnische Universität MünchenMünchenGermany

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