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

Document Type : Research Paper

Authors

1 Department of Applied Mathematics‎, ‎Hakim Sabzevari University‎, ‎Sabzevar‎, ‎Iran‎.

2 Institute computational Mathematics‎, ‎Technische Universitat Braunschweig‎, ‎D-38106 Braunschweig‎, ‎Germany.

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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Main Subjects

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### History

• Receive Date: 02 January 2016
• Revise Date: 26 May 2016
• Accept Date: 01 July 2016
• First Publish Date: 31 October 2017