The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented. AMS subject classification (2000): 15A18, 15A23, 65F35.

It has been recently proposed that the background independent open superstring field theory action is given by the disc partition function with all possible open string operators inserted at the boundary of the disc. We use this proposal to study tachyon condensation in the D0-D2 system. We evaluate the disc partition function for the D0-D2 system in presence of a large Neveu-Schwarz B-field us...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

In this paper, the performance of a subspace beamformer, namely the multiple signal classification algorithm (MUSIC), is scrutinized in the presence of sensor position errors. Based on a perturbation model, a relationship between the array autocorrelation matrix and the source autocorrelation matrix is established. It is shown that under certain assumptions on the source signals, the Gaussian s...

This paper develops a multiattribute preference ranking rule in the context of utility robustness. A nonparametric perturbation of a given additive reference utility function is specified to solve the problem of ambiguity and inconsistency in utility assessments, while preserving the additive structure and the decision maker’s risk preference under each criterion. A concept of robust preference...

The double angle theorems of Davis and Kahan bound the change in an invariant subspace when a Hermitian matrix A is subject to an additive perturbation A ! e A = A+A. This paper supplies analogous results when A is subject to a congruential, or multiplicative, perturbation A ! e A = D AD. The relative gaps that appear in the bounds involve the spectrum of only one matrix, either A or e A, in co...

Commercial organizations and government agencies that gather, store, share and disseminate data are facing increasing concerns over individual privacy and confidentiality. Confidential data is often masked in the database or prior to release to a third party, through methods such as data perturbation. In this study, reidentification risks of three major additive data perturbation techniques wer...