The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. This paper discusses application of the GMRES method to the solution of large linear systems of equations that arise from the discretization of linear ill-posed problems. These linear systems are severely ill-conditioned and are referred to as discrete ill...

This paper studies convergence properties of the block GMRES algorithm when applied to nonsymmetric systems with multiple right-hand sides. A convergence theory is developed based on a representation of the method using matrix-valued polynomials. Relations between the roots of the residual polynomial for block GMHES and the matrix &-pseudospectrum are derived, and illustrated with numerical exp...

Block Toeplitz matrices are a special class of that exhibit reduced memory requirements and complexity matrix-vector multiplications. We herein present an efficient computational approach to solve sequence block systems arising from system with multiple right-hand sides. Two different numerical schemes implemented for the solution based on global variants generalized minimal residual (GMRES) me...

Consider using the right-preconditioned GMRES (AB-GMRES) for obtaining minimum-norm solution of inconsistent underdetermined systems linear equations. Morikuni (Ph.D. thesis, 2013) showed that some and ill-conditioned problems, iterates may diverge. This is mainly because Hessenberg matrix in method becomes very so backward substitution resulting triangular system numerically unstable. We propo...

Abstract In this work, a new global-in-time solution strategy for incompressible flow problems is presented, which highly exploits the pressure Schur complement (PSC) approach construction of space–time multigrid algorithm. For linear like Stokes equations discretized in space using an inf-sup-stable finite element pair, fundamental idea to block systems associated with individual time steps in...

In this paper a distributed iterative GMRES algorithm for solving huge and sparse linear systems (that appear in the Markov chain analysis of queueing network models) is considered. It is implemented using the MPI standard on a collection of Linux machines and the emphasis is put upon the size of linear systems being solved and possibility of storing huge and sparse matrices as well as huge vec...

We investigate parallel algorithms for the solution of the shallow-water equation in a space-time framework. For periodic solutions, the discretized problem can be written as a large cyclic non-linear system of equations. This system of equations is solved with a Newton iteration which uses two levels of preconditioned GMRES solvers. The parallel performance of this algorithm is illustrated on ...

in this paper, we have proposed a new algorithm which combines pso and ga in such a way that the new algorithm is more effective and efficient.the particle swarm optimization (pso) algorithm has shown rapid convergence during the initial stages of a global search but around global optimum, the search process will become very slow. on the other hand, genetic algorithm is very sensitive to the in...

Boundary value methods (BVMs) for ordinary di erential equations require the solution of nonsymmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditio...