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Relaxation methods for the computation of the spectral norm

Applications And Special Topics

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Part of the Lecture Notes in Mathematics book series (LNM,volume 953)

Abstract

Relaxation methods of H.R. Schwarz and A. Ruhe are used for the computation of the spectral norm σ1 of an arbitrary m×n-matrix A (i.e., σ1 is the maximal singular value of A). σ1 is eigenvalue and spectral radius of a symmetric weakly two-cyclic matrix Â. Using this fact, results on the optimal (asymptotic) relaxation factor ωo are derived. Further it is shown that using ωo from the beginning of the algorithm often prevents a rapid convergence. A strategy for the choice of ω is presented.

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References

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© 1982 Springer-Verlag

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Kolb, G., Niethammer, W. (1982). Relaxation methods for the computation of the spectral norm. In: Ansorge, R., Meis, T., Törnig, W. (eds) Iterative Solution of Nonlinear Systems of Equations. Lecture Notes in Mathematics, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069380

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  • DOI: https://doi.org/10.1007/BFb0069380

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11602-8

  • Online ISBN: 978-3-540-39379-5

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