Deflated Restarting for Matrix Functions

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

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 nonsymmetric or non-Hermitian linear systems. First we recall the main features of flexible generalized minimum residual with...

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...

Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides

A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...

Flexible GMRES with Deflated Restarting

GMRES with Deflated Restarting

A modification is given of the GMRES iterative method for nonsymmetric systems of linear equations. The new method deflates eigenvalues using Wu and Simon’s thick restarting approach. It has the efficiency of implicit restarting, but is simpler and does not have the same numerical concerns. The deflation of small eigenvalues can greatly improve the convergence of restarted GMRES. Also, it is de...