Let T be a symmetric tridiagonal matrix with entries and eigenvalues of di¤erent magnitudes. For some T , small entry-wise relative perturbations induce small errors in the eigenvalues, independently of the size of the entries of the matrix; this is certainly true when the perturbed matrix can be written as e T = XTTX, with small jjXTX Ijj. Even if it is not possible to express in this way the ...

Privacy is becoming an increasingly important issue in many data mining applications. This has triggered the development of many privacy preserving data mining techniques. A frequently used disclosure protection method is data perturbation. When used for data mining, it is desirable that perturbation preserves statistical relationships between attributes, while providing adequate protection for...

The multiplicative perturbation bounds for weighted unitary polar factor are considered in the weighted unitary invariant norm, weighted spectral norm, and weighted Frobenius norm in this paper. As the special cases, new bounds for subunitary and unitary polar factor are also derived. These new bounds improve the corresponding results published recently to some extent. Mathematics subject class...

We propose a modiied approach to the abstract convergence theory of the additive and multiplicative Schwarz iterative methods associated with a subspace splitting for solving symmetric positive deenit linear problems. In particular, we obtain a satisfactory bound for the convergence rate of the appropriately scaled multiplicative Schwarz method directly in terms of the condition number of the c...

Given an eigenvalue of a symplectic matrix, we analyze its change under small structure-preserving perturbations, i.e., perturbations which maintain the symplectic nature of the matrix. Modelling such perturbations multiplicatively allows us to make use of the first order multiplicative perturbation theory developed in [2] via Newton diagram techniques. This leads to both leading exponents and ...

In this paper, we address the problem of sparse signal reconstruction using compressive sampling (CS) in the presence of unknown multiplicative perturbations. Such perturbations cause mismatch between the true signal basis and that in the measurements. We propose an algorithm which iteratively determines active bases, estimates the mismatch in the identified active bases, and adjusts the CS rec...

Multivariate multiple linear regression (MMLR), which occurs in a number of practical applications, generalizes traditional least squares (multivariate regression) to right-hand sides. We extend recent MLR analyses sketched MMLR general Schatten p-norms by interpreting the problem as multiplicative perturbation. Our work represents an extension Maher's results on p-norms. derive expressions for...

The Boussinesq equation is a mathematics model of thermohydraulics, which consists of equations of fluid and temperature in the Boussinesq approximation.The deterministic case has been studied systematically by many authors (e.g., see [1– 3]). However, in many practical circumstances, small irregularity has to be taken into account.Thus, it is necessary to add to the equation a random force, wh...