A class of product-type Krylov-subspace methods for solving nonsymmetric linear systems

Krylov subspace methods for solving linear systems

A Mixed Product Krylov Subspace Method for Solving Nonsymmetric Linear systems

In this paper, a product Krylov subspace method that we call mixed BiCGSTABCGS is derived. The method is built on the idea of the standard CGS and BiCGSTAB iterations but allows switching between the two at each iteration. This flexibility can be used, for example, to address the difficulty of excessive increase in residual norm in CGS, which may cause instability. In particular, a CGS based im...

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...

Krylov Subspace Methods for Linear Systems with Tensor Product Structure

The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a d-dimensional hypercube. Linear systems with tensor product structure can be regarded as linear matrix equations for d = 2 and appear to be their most natural extension for d > 2. A standard Krylov subspace...

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...