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Abstract: A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of Byers and confirms that ill-conditioned iterates may cause numerical instability. (Update)
Context of citations to this paper: More
.... in the Newton iteration for computing the matrix sign function and the subsequent spectral decomposition have been studied in [3, 8]. Recently, 1450 BAI, DEMMEL, DONGARRA, PETITET, ROBINSON, AND STANLEY an inverse free method for achieving better numerical stability...
...where l # is the length of the closed contour #. Recently, an asymptotic perturbation bound of sign(A) was given by Byers, He, and Mehrmann [13]. They show that to first order in #A #sign(A #A) sign(A)# # 4 # # 1 #A 12 # # # 2 ##A#, 9) where A is assumed to have the...
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BibTeX entry: (Update)
R. Byers, C. He, and V. Mehrmann. The matrix sign function method and the computation of invariant subspaces. Technical report, TU Chemnitz, Germany, 1994. To appear in SIAM J. Matrix Anal. Appl. http://citeseer.ist.psu.edu/byers94matrix.html More
@article{ byers97matrix,
author = "Ralph Byers and Chunyang He and Volker Mehrmann",
title = "The Matrix Sign Function Method and the Computation of Invariant Subspaces",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "18",
number = "3",
pages = "615--632",
year = "1997",
url = "citeseer.ist.psu.edu/byers94matrix.html" }
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