Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...

We study the Majorization arrow in a big class of quantum adiabatic algorithms. In a quantum adiabatic algorithm, the ground state of the Hamiltonian is a guide state around which the actual state evolves. We prove that for any algorithm of this class, step-by-step majorization of the guide state holds perfectly. We also show that step-by-step majorization of the actual state appears if the run...

Most of the statistical estimation procedures are based on a quite simple principle: find the distribution that, within a certain class, is as similar as possible to the empirical distribution, obtained from the sample observations. This leads to the minimization of some statistical functionals, usually interpreted ad measures of distance or divergence between distributions. In this paper we st...

Majorization is a powerful, easy-to-use and exible tool which arises frequently in quantum mechanics as a consequence of fundamental connections between unitarity and the majorization relation. Entanglement theory does not escape from its in uence. Thus the interconversion of bipartite pure states by means of local manipulations turns out to be ruled to a great extend by majorization relations....

This paper considers the problem of constructing a multidimensional Lorenz dominance relation (MLDR) satisfying normatively acceptable conditions. One of the conditions, Comonotonizing Majorization (CM), is a weaker form of the condition of Correlation Increasing Majorizaton considered in the literature on multidimensional inequality indices. A condition, called Prioritization of Attributes und...

We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to the circumferences of a set of concentric circles around the origin. Such constraints frequently occur in the layout of social or policy networks, when structural centrality is mapped to geometric centrality, or when the primary intention of the layout is the display of the vicinity of a distingui...

A majorization relating the singular values of an oo-diagonal block of a Hermitian matrix and its eigenvalues is obtained. This basic majorization inequality implies various new and existing results.

This paper presents majorization results for PH-generators. Based on the majorization results, bounds on the moments and Laplace-Stieltjes transforms of phase-type distributions are found. Exponential distributions and Coxian distributions are identified to be extremal PH-distributions with respect to all the moments and Laplace-Stieltjes transforms for certain subsets of PH-distributions. UN C...

We study the conceptmatrix majorization: for two real matrices A and B having m rows we say that A majorizes B if there is a row-stochastic matrix X with AX = B. A special case is classical notion of vector majorization. Several properties and characterizations of matrix majorization are given. Moreover, interpretations of the concept in mathematical statistics are discussed and some combinator...

let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...