The growth factor and efficiency of Gaussian elimination with rook pivoting

Some Features of Gaussian Elimination with Rook Pivoting

Rook pivoting is a relatively new pivoting strategy used in Gaussian elimination (GE). It can be as computationally cheap as partial pivoting and as stable as complete pivoting. This paper shows some new attractive features of rook pivoting. We first derive error bounds for the LU factors computed by GE and show rook pivoting usually gives a highly accurate U factor. Then we show accuracy of th...

Some Features of Gaussian Elimination with Rook Pivoting

Large growth factors in Gaussian elimination with pivoting

The growth factor plays an important role in the error analysis of Gaussian elimination. It is well known that when partial pivoting or complete pivoting is used the growth factor is usually small, but it can be large. The examples of large growth usually quoted involve contrived matrices that are unlikely to occur in practice. We present real and complex n n matrices arising from practical app...

Threshold-pivoting in parallel Gaussian elimination for improved efficiency

The use of threshold pivoting with the purpose to reduce fill-in during sparse Gaussian elimination has been generally acknowledged. Here we describe the application of threshold pivoting in dense Gaussian elimination for improving the performance of a parallel implementation. We discuss the effect on the numerical stability and conclude that the consequences are only of minor importance as lon...

Gaussian Elimination with Randomized Complete Pivoting

Gaussian elimination with partial pivoting (GEPP) has long been among the most widely used methods for computing the LU factorization of a given matrix. However, this method is also known to fail for matrices that induce large element growth during the factorization process. In this paper, we propose a new scheme, Gaussian elimination with randomized complete pivoting (GERCP) for the efficient ...