Perturbation analysis of singular subspaces
and deflating subspaces |
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Authors: | Ji-guang Sun |
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Affiliation: | Department of Computing Science,
Ume? University,
S-901 87 Ume?, Sweden; e-mail: jisun@cs.umu.se, SE
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Abstract: | Summary.
Perturbation expansions for singular subspaces of a matrix
and for deflating subspaces of a regular matrix pair are derived
by using a technique previously described by the author. The
perturbation expansions are then used to derive Fr\'echet derivatives,
condition numbers, and
th-order
perturbation bounds for the subspaces.
Vaccaro's result on second-order perturbation expansions for a special
class of singular subspaces can be obtained from a general result of this
paper. Besides, new perturbation bounds for singular subspaces
and deflating subspaces are derived
by applying a general theorem on solution of a system of nonlinear
equations. The results of this paper reveal an important fact: Each singular
subspace and each deflating subspace have individual perturbation bounds
and individual condition numbers.
Received July 26, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 65F35 |
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