Add to ORKGWe show that the stability of Gaussian elimination with partial pivoting relates to the well definition of the reduced triangular systems. We develop refined perturbation bounds that generalize Skeel bounds to the case of ill conditioned systems. We finally develop reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems
Several parallel algorithms have been proposed for the solution of triangular systems. The stability...
It has been recently shown that large growth factors might occur in Gaussian Elimination with Partia...
this paper, the wrap-around partitioning methodology, originally proposed by Hegland [1], is conside...
We show that the stability of Gaussian elimination with partial pivoting relates to the well definit...
In this paper we present three different pivoting strategies for solving general tridiagonal systems...
In this paper we present new formulas for characterizing the sensitivity of tridiagonal systems that...
If $\hat{x}$ is the computed solution to a tridiagonal system $Ax = b$ obtained by Gaussian elimina...
AbstractUsing the simple vehicle of tridiagonal Toeplitz matrices, the question of whether one must ...
Abstract. Matrices, called ε-BD matrices, that have a bidiagonal decomposition satisfying some sign ...
The stability of the Gauss-Jordan algorithm with partial pivoting for the solution of general system...
For the solution of a linear system Ax = b using Gaussian elimination, some new properties of scaled...
This paper considers elimination methods to solve dense linear systems, in particular a variant of G...
If $\hat x$ is the computed solution to a tridiagonal system $Ax = b$ obtained by Gaussian eliminati...
In this paper, the numerical aspects of some methods for the solution of bidiagonal systems are anal...
Abstract. A signicant collection of two-point boundary value problems is shown to give rise to linea...
Several parallel algorithms have been proposed for the solution of triangular systems. The stability...
It has been recently shown that large growth factors might occur in Gaussian Elimination with Partia...
this paper, the wrap-around partitioning methodology, originally proposed by Hegland [1], is conside...
We show that the stability of Gaussian elimination with partial pivoting relates to the well definit...
In this paper we present three different pivoting strategies for solving general tridiagonal systems...
In this paper we present new formulas for characterizing the sensitivity of tridiagonal systems that...
If $\hat{x}$ is the computed solution to a tridiagonal system $Ax = b$ obtained by Gaussian elimina...
AbstractUsing the simple vehicle of tridiagonal Toeplitz matrices, the question of whether one must ...
Abstract. Matrices, called ε-BD matrices, that have a bidiagonal decomposition satisfying some sign ...
The stability of the Gauss-Jordan algorithm with partial pivoting for the solution of general system...
For the solution of a linear system Ax = b using Gaussian elimination, some new properties of scaled...
This paper considers elimination methods to solve dense linear systems, in particular a variant of G...
If $\hat x$ is the computed solution to a tridiagonal system $Ax = b$ obtained by Gaussian eliminati...
In this paper, the numerical aspects of some methods for the solution of bidiagonal systems are anal...
Abstract. A signicant collection of two-point boundary value problems is shown to give rise to linea...
Several parallel algorithms have been proposed for the solution of triangular systems. The stability...
It has been recently shown that large growth factors might occur in Gaussian Elimination with Partia...
this paper, the wrap-around partitioning methodology, originally proposed by Hegland [1], is conside...