Abstract
It is presented a new technique to estimate the condition number of additive preconditioners. This technique leads to small bounds of the condition number. We apply this technique to the BPX preconditioner on a tensor product grid.
It is proved that the lower eigenvalue of this preconditioner is larger than 0.0717. Using the standard approach for estimating the upper eigenvalue, shows that the upper eigenvalue is smaller than 37.7. This implies that the condition number of the BPX preconditioner is smaller than 526. This estimation implies that 16 cgiterations applied to the BPX preconditioner reduce the algebraic error by a factor 0.233 independent of the number of levels. This also holds for domains with reentrant corners.
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© 2000 Springer-Verlag Berlin Heidelberg
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Pflaum, C. (2000). Estimation of the Condition Number of Additive Preconditioners on Tensor Product Grids. In: Dick, E., Riemslagh, K., Vierendeels, J. (eds) Multigrid Methods VI. Lecture Notes in Computational Science and Engineering, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58312-4_28
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DOI: https://doi.org/10.1007/978-3-642-58312-4_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67157-2
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