The row/column pivoting strategy on multicomputers

On multicomputers the partial pivoting phase of the LU factorization has a peculiar load unbalancing due to the presence of idle processors in most matrix decompositions. Moreover, intrinsic synchronization barriers do not allow a complete masking of this overhead by means of pipelining techniques. We propose to reduce load unbalancing by ‘assigning extra work to idle processors’; this leads to a new pivoting strategy, named row/column pivoting, which is mainly attractive to 2D decompositions. Row/column pivoting furnishes an LU factorization algorithm that guarantees better numerical stability at the same cost of partial pivoting in case of square decomposition. A further improvement is achieved by adding pipelining schemes to the naive form. In the design of the algorithms and in their evaluation we have adopted a new environment that allows a decomposition-independent parallel programming.