Abstract
The ScaLAPACK library contains a pair of routines for solving banded linear systems which are strictly diagonally dominant by rows. Mathematically, the algorithm is complete block cyclic reduction corresponding to a particular block partitioning of the system. In this paper we extend Heller’s analysis of incomplete cyclic reduction for block tridiagonal systems to the ScaLAPACK case. We obtain a tight estimate on the significance of the off diagonal blocks of the tridiagonal linear systems generated by the cyclic reduction algorithm. Numerical experiments illustrate the advantage of omitting all but the first reduction step for a class of matrices related to high order approximations of the Laplace operator.
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References
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Kjelgaard Mikkelsen, C.C., Kågström, B. (2012). Incomplete Cyclic Reduction of Banded and Strictly Diagonally Dominant Linear Systems. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31464-3_9
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DOI: https://doi.org/10.1007/978-3-642-31464-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31463-6
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