In this paper, we consider large-scale linear discrete ill-posed problems where the right-hand side contains noise. Regularization techniques such as Tikhonov regularization are needed to control the effect of the noise on the solution. In many applications such as in image restoration the coefficient matrix is given as a Kronecker product of two matrices and then Tikhonov regularization proble...

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.

In large-scale scienti c computing, linear sparse solver is one of the most time-consuming process. In GeoFEM, various types of preconditioned iterative method is implemented on massively parallel computers. It has been well-known that ILU(0) factorization is very e ective preconditioning method for iterative solver. But it's also well-known that this method requires global data dependency and ...

The global FOM and GMRES are among the effective algorithms to solve linear system of equations with multiple right-hand sides. In this paper, we study these algorithms in the case that the coefficient matrix is symmetric and extract two CGtype algorithms for solving symmetric linear systems of equations with multiple right– hand sides. Then, we compare the numerical performance of the new algo...

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.