A new relative perturbation theorem for singular subspaces

Submitted by H. Schneider
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Abstract

This note addresses the sensitivity of singular subspaces of a matrix under relative perturbations. It employs a new technique of separating a multiplicative perturbation D into two components: one is the distance of a scalar multiple of D to the nearest unitary matrix Q and the other is the distance of Q to the identity. Consequently, the new bounds reflect the intrinsic differences in how left and right multiplicative perturbations affect left and right singular subspaces.

MSC

15A18
15A42
65F15
65F35
65G99

Keywords

Multiplicative perturbation
Relative perturbation theory
Relative gap
Singular subspace

Cited by (0)

1

This work was supported in part by the National Science Foundation under Grant No. ACI-9721388 and by the National Science Foundation CAREER award under Grant No. CCR-9875201

2

This work was supported in part by the National Science Foundation under Grant No. 970909-8426.