A Flexible Generalized Conjugate Residual Method with Inner Orthogonalization and Deflated Restarting

A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics

This work is concerned with the development and study of a minimum residual norm subspace method based on the Generalized Conjugate Residual method with inner Orthogonalization (GCRO) method that allows flexible preconditioning and deflated restarting for the solution of non-symmetric or non-Hermitian linear systems. First we recall the main features of Flexible Generalized Minimum Residual wit...

Flexible GMRES with Deflated Restarting

Pii: S0168-9274(01)00107-6

We discuss a general framework for generalized conjugate gradient methods, that is, iterative methods (for solving linear systems) that are based on generating residuals that are formally orthogonal to each other with respect to some true or formal inner product. This includes methods that generate residuals that are minimal with respect to some norm based on an inner product. A similar, even m...

A Simplified and Flexible Variant of GCROT for Solving Nonsymmetric Linear Systems

There is a need for flexible iterative solvers that can solve large-scale (> 106 unknowns) nonsymmetric sparse linear systems to a small tolerance. Among flexible solvers, flexible GMRES (FGMRES) is attractive because it minimizes the residual norm over a particular subspace. In practice, FGMRES is often restarted periodically to keep memory and work requirements reasonable; however, like resta...

A Restarted Gmres Method Augmented with Eigenvectors * Ronald

The GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restart. It is proposed that approximate eigenvectors corresponding to a few of the smallest eigenvalues be formed and added to the subspace...