We apply algebraic multigrid (AMG) as a preconditioner for solving large singular linear systems of the type (I−T T )x = 0 with GMRES. Here, T is assumed to be the transition matrix of a Markov process. Although AMG and GMRES are originally designed for the solution of regular systems, with adequate adaptation their applicability can be extended to problems as described above.

A new family of iterative block methods, the family of block EN-like methods, is introduced. EEcient versions are presented. Computational complexity, memory requirements and convergence properties are investigated. Finally, numerical results are presented, which show a lot of promise for the new methods, also in comparison to block GMRES and a hybrid block GMRES scheme.

Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed at each iteration step by a suitable approximation process, e.g., by GMRES itself.

In this article, we compare different iterative techniques enhanced by the CBFM, which are used to analyze finite arrays of disjoint antenna elements. These based on stationary-type methods (Jacobi, Gauss–Seidel, and macroblock Jacobi), nonstationary GMRES, hybrid alternating GMRES-Jacobi (AGJ) method that combines these two types. each iteration, reduced CBFM system is constructed previous ite...

In this paper, we consider a family of algorithms, called IDR, based on the induced dimension reduction theorem. IDR is efficient short recurrence methods introduced by Sonneveld and Van Gijzen for solving large systems nonsymmetric linear equations. These generate residual vectors that live in sequence nested subspaces. We present IDR(s) method give two improvements its convergence. also defin...

We present a polynomial preconditioner for solving large systems of linear equations. The is derived from the minimum residual (the GMRES polynomial) and more straightforward to compute implement than many previous preconditioners. Our current implementation this using its roots naturally stable methods computing same polynomial. further stability control added roots, allows high degree polynom...

Three solvers for saddle point problems arising from the linearization and discretization of the steady state incompressible Navier–Stokes equations are numerically studied. The numerical tests are based on nonconforming finite element approximations of lowest order in two–dimensional domains using isotropic meshes. The investigated solvers are coupled multigrid methods with Vanka–type smoother...

The anisotropic and active properties of the perfectly matched layer (PML) absorbers significantly deteriorate the finite-element method (FEM) system condition and as a result, convergence of the iterative solver is substantially affected. To address this issue, we examine the generalized minimal residual (GMRES) solver for solving finite-element systems terminated with PML. A strong approximat...