Quasi-minimal residual smoothing technique for the IDR($s$) method

The Improved Quasi - Minimal Residual

For the solutions of linear systems of equations with unsymmetric coeecient matrices, we propose an improved version of the quasi-minimal residual (IQMR) method by using the Lanczos process as a major component combining elements of numerical stability and parallel algorithm design. For Lanczos process, stability is obtained by a coupled two-term procedure that generates Lanczos vectors normali...

Minimal Residual Smoothing in Multi-Level Iterative Method

Minimal Residual Smoothing in Multi-Level Iterative Method

A minimal residual smoothing (MRS) technique is employed to accelerate the convergence of the multi-level iterative method by smoothing the residuals of the original iterative sequence. The sequence with smoothed residuals is reintroduced into the multi-level iterative process. The new sequence generated by this acceleration procedure converges much faster than both the sequence generated by th...

Performance Evaluation of the Improved Quasi - Minimal Residual Method

For the solutions of linear systems of equations with unsym-metric coeecient matrices, we have proposed an improved version of the quasi-minimal residual (IQMR) method 18] by using the Lanczos process as a major component combining elements of numerical stability and parallel algorithm design. For Lanczos process, stability is obtained by a couple two-term procedure that generates Lanczos vecto...

FQMR: A Flexible Quasi-Minimal Residual Method with Inexact Preconditioning

A flexible version of the QMR algorithm is presented which allows for the use of a different preconditioner at each step of the algorithm. In particular, inexact solutions of the preconditioned equations are allowed, as well as the use of an (inner) iterative method as a preconditioner. Several theorems are presented relating the norm of the residual of the new method with the norm of the resid...