On the backward stability of Gauss-Jordan elimination

Abstract

--ZusammenfassungOn the Backward Stability of Gauss-Jordan Elimination. Backward stability of Gauss-Jordan elimination is discussed. The method proposed in [4] with some modifications is used. The basic tool of this method is the graph of the algorithm and its parallel structure. The system Ux = c, where U is an n x n upper triangular matrix, is considered for simplicity. Then estimates of the equivalent perturbations depending quadratically on n are obtained.