Deflation in Krylov subspace methods and distance to uncontrollability

Deflation in Krylov Subspace Methods and Distance to Uncontrollability

The task of extracting from a Krylov decomposition the approximation to an eigenpair that yields the smallest backward error can be phrased as finding the smallest perturbation which makes an associated matrix pair uncontrollable. Exploiting this relationship, we propose a new deflation criterion, which potentially admits earlier deflations than standard deflation criteria. Along these lines, a...

Deflation and Balancing Preconditioners for Krylov Subspace Methods Applied to Nonsymmetric Matrices

For quite some times, deflation preconditioner has been proposed and used to accelerate the convergence of Krylov subspace methods. For symmetric positive definite linear systems, convergence of CG combined with deflation has been analyzed and compared with other preconditioners, e.g. with the abstract balancing preconditioner [Nabben and Vuik, SIAM J. Sci. Comput., 27 (2006), pp. 1742–1759]. I...

Avoiding Krylov Subspace Methods

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Communication-avoiding Krylov subspace methods

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Krylov subspace methods in the electronic industry