Rafiei, A., Bollhoefer, M. (2017). Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process. Bulletin of the Iranian Mathematical Society, 43(5), 1417-1456.

A. Rafiei; M. Bollhoefer. "Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process". Bulletin of the Iranian Mathematical Society, 43, 5, 2017, 1417-1456.

Rafiei, A., Bollhoefer, M. (2017). 'Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process', Bulletin of the Iranian Mathematical Society, 43(5), pp. 1417-1456.

Rafiei, A., Bollhoefer, M. Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process. Bulletin of the Iranian Mathematical Society, 2017; 43(5): 1417-1456.

Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process

Receive Date: 02 January 2016,
Revise Date: 26 May 2016,
Accept Date: 01 July 2016

Abstract

In this paper, we use a complete pivoting strategy to compute the IUL preconditioner obtained as the by-product of the Backward Factored APproximate INVerse process. This pivoting is based on the complete pivoting strategy of the Backward IJK version of Gaussian Elimination process. There is a parameter $\alpha$ to control the complete pivoting process. We have studied the effect of different values of $\alpha$ on the quality of the IUL preconditioner. For the numerical experiments section, the IUL factorization which is coupled with the complete pivoting is compared to the ILUTP and to the left-looking version of RIF which is coupled with the complete pivoting strategy. As the preprocessing, we have applied the maximum weighted matching coupled the Reverse Cuthill-Mckee (RCM) and multilevel nested dissection reordering.

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