Motivations and realizations of Krylov subspace methods for large sparse linear systems

The Improved Krylov Subspace Methods for Large and Sparse Linear Systems on Bulk Synchronous Parallel Architecture

In this paper, we would like to summarize the recent advances on the improved Krylov Subspace methods for the solutions of large and sparse linear systems of equations with unsymmetric coefficient matrices. The proposed methods combine elements of numerical stability and parallel algorithm design without increasing much computational costs. The methods have the following common feature that all...

Krylov subspace methods for solving linear systems

Inexact Krylov Subspace Methods for Linear Systems

There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming approximation method is necessary to compute it with some prescribed relative precision. In this paper we investigate the effect of an approximately computed matrix-vector product on the convergence and accuracy of several Krylov subspace solvers. The obtained insi...

Recent computational developments in Krylov subspace methods for linear systems

Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed. These new developments include different versions of restarted, augmented, deflated, flexible, nested, and inexact methods. Also reviewed are methods specifically tailored to systems with special properties such as special forms of symmetry and...

On Squaring Krylov Subspace Iterative Methods for Nonsymmetric Linear Systems

The Biorthogonal Lanczos and the Biconjugate Gradients methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld [19] obtained the Conjugate Gradient Squared by squaring the matrix polynomials of the Biconjugate Gra­ dients method. Here we square the Biorthogonal Lanczos, the Biconjugate Residual and the Biconjugate Orth...