Numerically safe Gaussian elimination with no pivoting

Numerically Safe Gaussian Elimination with No Pivoting

Gaussian elimination with partial pivoting is performed routinely, millions times per day around the world, but partial pivoting (that is, row interchange of an input matrix) is communication intensive and has become the bottleneck of the elimination algorithm in the present day computer environment, in both cases of matrices of large and small size. Gaussian elimination with no pivoting as wel...

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 ...

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

On the Parallel Complexity of Gaussian Elimination with Pivoting

Consider the Gaussian Elimination algorithm with the well-known Partial Pivoting strategy for improving numerical stability (GEPP). Vavasis proved that the problem of determining the pivot sequence used by GEPP is log space-complete for P, and thus inherently sequential. Assuming P 6 = NC, we prove here that either the latter problem cannot be solved in parallel time O(N 1=2?) or all the proble...