Multiplicative backward stability results are presented for two algorithms which compute the singular value decomposition of dense matrices. These algorithms are the classical onesided Jacobi algorithm, with a stringent stopping criterion, and an algorithm which uses one-sided Jacobi to compute high accurate singular value decompositions of matrices given as rank-revealing factorizations. When ...

Heart rate variability is assumed to result from a multiplicative or cascade mechanism based on its multifractal property. Numerical results on the perturbation of the cascade are given to compare HRV under parasympathetic (PNS) and sympathetic (SNS) autonomic blockades. It was found that qualitative change of the HRV multifractal, which was observed in PNS blockade, is due to the change from a...

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

Any unperturbed and perturbed posterior density can formally be linked by a mixture. Many divergences between the unperturbed and perturbed posterior density global measures of influence of the perturbation are then essentially determined by the Fisher information with respect to the mixing parameter evaluated at the unperturbed density. It is investigated which aspect of change this Fisher inf...

In this note, we obtain a new multiplicative perturbation theorem for local Cregularized cosine function with a nondensely defined generator A. An application to an integrodifferential equation is given.

We focus primarily on the use of additive and matrix multiplicative data perturbation techniques in privacy preserving data mining (PPDM). We survey a recent body of research aimed at better understanding the vulnerabilities of these techniques. These researchers assumed the role of an attacker and developed methods for estimating the original data from the perturbed data and any available prio...

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0, 1}n → Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions ...