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It is well known that some pivoting strategies are backward stable for Gauss elimination but are not backward stable for Gauss–Jordan elimination (GJE) when these procedures are used to solve a linear system Ax=b. We analyse the simultaneous backward stability for Gauss and GJE of several pivoting strategies, including a pivoting strategy which we call double partial pivoting. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we introduce and analyse a new Schur complement approximation based on incomplete Gaussian elimination. The approximate Schur complement is used to develop a multigrid method. ibis multigrid method has an algorithmic structure that is very similar to the algorithmic structure of classical multigrid methods. The resulting method is almost purely algebraic and has increasing robustness properties with respect to variation in problem parameters. [ABSTRACT FROM AUTHOR]

In this paper we present a novel improvement of Wilkinson's iterative refinement for the solution of linear system by using stability results of numerical solution for a dynamic system associated with the linear system. The convergence analysis is shown and roundoff error analysis is considered for this new refinement. Numerical experiments are accompanied to support our analysis. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We devise a fast fraction-free algorithm for the computation of the triangular factorization of Bernstein–Bezoutian matrices with entries over an integral domain. Our approach uses the Bareiss fraction-free variant of Gaussian elimination, suitably modified to take into account the structural properties of Bernstein–Bezoutian matrices. The algorithm can be used to solve problems in algebraic geometry that arise in computer aided geometric design and computer graphics. In particular, an example of the application of this algorithm to the numerical computation of the intersection points of two planar rational Bézier curves is presented. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]