ML(n)BiCGStab is a Krylov subspace method for the solution of large, sparse and non-symmetric linear systems. In theory, it is a method that lies between the well-known BiCGStab and GMRES/FOM. In fact, when n = 1, ML(1)BiCGStab is BiCGStab and when n = N, ML(N)BiCGStab is GMRES/FOM where N is the size of the linear system. Therefore, ML(n)BiCGStab is a bridge that connects the Lanczos-based BiC...

FOM and GMRES are Krylov subspace iterative methods for solving nonsymmetric linear systems. The Ritz values are approximate eigenvalues, which can be computed cheaply within these algorithms. In this paper, we generalise the concept of Harmonic Ritz values, introduced by Paige et al. for symmetric matrices, to nonsymmetric matrices. We show that the zeroes of the residual polynomials of FOM an...

This paper discusses how to control the accuracy of inexact matrix-vector products in restarted GMRES. We will show that the GMRES iterations can be performed with relatively low accuracy. Furthermore, we will study how to compute the residual at restart and propose suitable strategies to control the accuracy of the matrix-vector products in this computation.

Several variants of the GMRES method for solving linear nonsingular systems of algebraic equations are described. These variants diier in building up diierent sets of orthonormalized vectors used for the construction of the approximate solution. A new A T A-variant of GMRES is proposed and the eecient implementation of the algorithm is discussed.

A semi-iterative method based on a nested application of Flexible Generalized Minimum Residual(FGMRES) was developed to solve the linear systems resulting from the application of the discretized two-phase hydrodynamics equations to nuclear reactor transient problems. The complex three-dimensional reactor problem is decomposed into simpler, more manageable problems which are then recombined sequ...