Further analysis of the quadrant interlocking factorisation (Q.I.F.) method

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Abstract
New parallel methods based on quadrant interlocking factorisation (Q.I.F.) suitable for the solution of linear systems have recently been developed in which interlocking matrix quadrant factors of “butterfly form” are considered instead of the standard LU triangular factors of the coefficient matrix, i.e., Evans and Hatzopoulos [1], Evans and Hadjidimos [2] and Shanehchi [3]. In this paper, we present an error analysis for the parallel algorithm with a choice of pivoting strategies and introduce a Gauss-Jordan form of the parallel algorithm, the block form of which represents an efficient algorithmic strategy for use on MIMD machines, i.e., asynchronous multiprocessors with shared memory.

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