A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
SIAM Journal on Scientific Computing
Eigenvalue perturbation bounds for Hermitian block tridiagonal matrices
Applied Numerical Mathematics
On aggressive early deflation in parallel variants of the QR algorithm
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
dqds with Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
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Aggressive early deflation has proven to significantly enhance the convergence of the QR algorithm for computing the eigenvalues of a nonsymmetric matrix. One purpose of this paper is to point out that this deflation strategy is equivalent to extracting converged Ritz vectors from certain Krylov subspaces. As a special case, the single-shift QR algorithm enhanced with aggressive early deflation corresponds to a Krylov subspace method whose starting vector undergoes a Rayleigh-quotient iteration. It is shown how these observations can be used to derive improved convergence bounds for the QR algorithm.