In this paper, the diagonal majorization algorithm (DMA) has been investigated. The research focuses on the possibilities to increase the efficiency of the algorithm by disclosing its properties. The diagonal majorization algorithm is oriented at the multidimensional data visualization. The experiments have proved that, when visualizing large data set with DMA, it is possible to save the comput...

This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present a general majorization framework for assessing designs, which includes a stringent criterion of majorization via pairwise coincidences and flexible surrogates via convex functions. Classical orthogo...


 In this paper, we give a complete, explicit and constructive solution to the double generalized majorization problem. Apart from purely combinatorial interest, problem has strong impact in Matrix Pencils Completion Problems, Bounded Rank Perturbation it additional nice interpretation Representation Theory of Kronecker Quivers.

This paper establishes a strong connection between evolutionary algorithms and majorization theory, using replicator models as a bridge. The relationship between replicator selection systems and majorization theory suggests new selection operators, convergence results and theoretical gains such as the availability of convergence results from the well developed theory of inhomogeneous doubly sto...

Miranda-Thompson majorization is a group-induced cone ordering on $mathbb{R}^{n}$ induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For $X$, $Yin M_{m,n}$, $X$ is said to be  Miranda-Thompson majorized by $Y$ (denoted by $Xprec_{mt}Y$) if there exists some $Din rm{Conv(G)}$ s...

We explore the combinatorial properties of a particular type of extension monoid product of preinjective Kronecker modules. The considered extension monoid product plays an important role in matrix completion problems. We state theorems which characterize this product in both implicit and explicit ways and we prove that the conditions given in the definition of the generalized majorization are ...

This paper presents applications of a remarkable majorization inequality due to Bapat and Sunder in three different areas. The first application is a proof of Hiroshima’s 2003 result which arises in quantum information theory. The second one is an extension of some eigenvalue inequalities that have been used to bound chromatic number of graphs. The third application is a simplified proof of a m...

Two new elementary proofs are given of Landau's Theorem on necessary and sufficient conditions for a sequence of integers to be the score sequence for some tournament. The first is related to existing proofs by majorization, but it avoids depending on any facts about majorization. The second is natural and direct. Both proofs are constructive, so they each provide an algorithm for obtaining a t...

We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition. Our result relies on the fact that states which are mixed by Hadamard operators at any stage of the computation only differ by a phase. This property is a consequence of the structure of the initial state and of the QFT, ba...