Low-rank factorization is used in many areas of computer science where one performs spectral analysis on large sensitive data stored in the form of matrices. In this paper, we study differentially private low-rank factorization of a matrix with respect to the spectral norm in the turnstile update model. In this problem, given an input matrix A ∈ Rm×n updated in the turnstile manner and a target...

ABSTRACT. In contemporary applied and computationalmathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent randommatrices. This quantity is controlled by the norm of the expected square of the randommatrix and the expectation of the maximum squared norm achieved by one of the summands; there is also aweak dependence on the dimension of the rand...

In this paper, the spectral expression of the frequency-limited H2-norm, firstly presented in [18], is extended to the case of LTI dynamical systems which are not diagonalizable. This extension is achieved by considering partial fraction decomposition of the transfer function associated to a system which is in a Jordan form. Besides, examples are presented to illustrate the behaviour of the fre...