The Effect of Aggressive Earl Deflation on the Convergence of the Qr Algorithm
نویسنده
چکیده
Aggressive early deflation [1] has proven to significantly enhance the convergence of the QR algorithm for computing the eigenvalues of a nonsymmetric matrix. It is shown 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 Rayleighquotient iteration. These observations are used to derive improved convergence bounds for the QR algorithm. Acknowledgement: Supported by a DFG Emmy Noether fellowship andin part by the Swedish Foundation for Strategic Research under the FrameProgramme Grant A3 02:128. References[1] K. Braman, R. Byers, and R. Mathias, The multishift QR algorithm. II, Aggres-sive early deflation, SIAM J. Matrix Anal. Appl., 23, 4 (2002), pp. 948–973.
منابع مشابه
The Effect of Aggressive Early Deflation on the Convergence of the QR Algorithm
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...
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