Parallel subspace correction methods for nearly singular systems

Subspace Correction Methods for Singular Systems

We investigate the application of minimal residual and orthogonal residualsubspace correction methods to singular linear systems Ax = b. Special em-phasis is put on the special case of Krylov subspace methods. If A has index 1(i.e., if all Jordan blocks associated with the eigenvalue λ = 0 of A are 1× 1)the behaviour of these iterative methods is well understood (see, e.g., ...

Parallel multisplitting methods for singular linear systems

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example. Keywords—singular H-matrix, linear systems, ...

Stabilization of Stochastic Iterative Methods for Singular and Nearly Singular Linear Systems

We consider linear systems of equations, Ax = b, with an emphasis on the case where A is singular. Under certain conditions, necessary as well as sufficient, linear deterministic iterative methods generate sequences {xk} that converge to a solution, as long as there exists at least one solution. This convergence property can be impaired when these methods are implemented with stochastic simulat...

Gmres on (nearly) Singular Systems

We consider the behavior of the GMRES method for solving a linear system Ax = b when A is singular or nearly so, i.e., ill conditioned. The (near) singularity of A may or may not affect the performance of GMRES, depending on the nature of the system and the initial approximate solution. For singular A, we give conditions under which the GMRES iterates converge safely to a least-squares solution...

Subspace Correction Methods for Eigenvalue Problems 313