A global multi-grid/GMRES solution methodology on distributed memory machines is successfully developed in this study. To preserve the effectiveness of the multigrid scheme, the grid partitioning is based on the communication graph of the coarsest grid, so that all levels of the multi-grids are located in the same zone (processor). Each node of the graph is weighted with the total number of the...

in this paper‎, ‎we study convergence behavior of the global fom (gl-fom) and global gmres (gl-gmres) methods for solving the matrix equation $axb=c$ where $a$ and $b$ are symmetric positive definite (spd)‎. ‎we present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual‎. ‎in particular‎, ‎the obtained upper...

Steepest descent preconditioning is considered for the recently proposed nonlinear generalized minimal residual (N-GMRES) optimization algorithm for unconstrained nonlinear optimization. Two steepest descent preconditioning variants are proposed. The first employs a line search, while the second employs a predefined small step. A simple global convergence proof is provided for the NGMRES optimi...

Through the research of the parallel computational model based on the principal and subordinate mode and the basic theory of Gmres Algorithm in Krylov subspace, this essay raises a improvement parallel Predict-Correct Gmres(m) algorithm which posses Predict-Correct pattern, and shows the computing examples for linear equations. After the comparison with the result from the new parallel Predict-...

Many problems in science and engineering field require the solution of shifted linear systems with multiple right hand sides and multiple shifts. To solve such systems efficiently, the implicitly restarted global GMRES algorithm is extended in this paper. However, the shift invariant property could no longer hold over the augmented global Krylov subspace due to adding the harmonic Ritz matrices...

In this paper, we propose an efficient parallel implementation of the GMRES method for GPU clusters. This implementation requires us to parallelize the GMRES algorithm between CPUs of the cluster. Hence, all parallel and intensive computations on local data are performed on GPUs and reduction operations to compute global results are carried out by CPUs. The performances of our parallel GMRES so...

This paper presents equivalent forms of the Sylvester matrix equations. These equivalent forms allow us to use block linear methods for solving large Sylvester matrix equations. In each step of theses iterative methods we use global FOM or global GMRES algorithm for solving an auxiliary block matrix equations. Also, some numerical experiments for obtaining the numerical approximated solution of...

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from ...

Recently, the complementary behavior of restarted GMRES has been studied. We observed that successive cycles of restarted block BGMRES (BGMRES(m,s)) can also complement one another harmoniously in reducing the iterative residual. In the present paper, this characterization of BGMRES(m,s) is exploited to form a hybrid block iterative scheme. In particular, a product hybrid block GMRES algorithm ...

Work on generalizing the deflated, restarted GMRES algorithm, useful in lattice studies using stochastic noise methods, is reported. We first show how the multi-mass extension of deflated GMRES can be implemented. We then give a deflated GMRES method that can be used on multiple right-hand sides of Ax = b in an efficient manner. We also discuss and give numerical results on the possibilty of co...