Subspace-by-subspace preconditioners for structured linear systems

Subspace-by-subspace preconditioners for structured linear systems

We consider the iterative solution of symmetric positive-de nite linear systems whose coe cient matrix may be expressed as the outer-product of low-rank terms. We derive suitable preconditioners for such systems, and demonstrate their e ectiveness on a number of test examples. We also consider combining these methods with existing techniques to cope with the commonly-occuring case where the coe...

Subspace Identification for Linear Systems

Krylov subspace methods for solving linear systems

Subspace-diskcyclic sequences of linear operators

A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

Inexact Krylov Subspace Methods for Linear Systems

There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming approximation method is necessary to compute it with some prescribed relative precision. In this paper we investigate the effect of an approximately computed matrix-vector product on the convergence and accuracy of several Krylov subspace solvers. The obtained insi...