In this paper, we obtain extensions of majorization type results and extensions of weighted Favard’s and Berwald’s inequality. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results and differences deduced from weighted Favard’s and Berwald’s inequality. This implies a surprising property of exponentially convexity and log-convexity of th...

A new notion of coneigenvalue was introduced by Ikramov in [Kh.D. Ikramov. On pseudo-eigenvalues and singular numbers of a complex square matrix (in Russian). Zap. Nauchn. Semin. POMI, 334:111–120, 2006.]. This paper presents some majorization inequalities for coneigenvalues, which extend some classical majorization relations for eigenvalues and singular values, and may serve as a basis for fur...

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...

The adoption of the stress-majorization method frommulti-dimensional scaling into graph layout has provided an improved mathematical basis and better convergence properties for so-called “force-directed placement” techniques. In this paper we give an algorithm for augmenting such stress-majorization techniques with orthogonal ordering constraints and we demonstrate several graphdrawing applicat...

A new notion of coneigenvalue was introduced by Ikramov in [On pseudo-eigenvalues and singular numbers of a complex square matrix, (in Russian), Zap. Nauchn. Semin. POMI 334 (2006), 111-120]. This paper presents some majorization inequalities for coneigenvalues, which extend some classical majorization relations for eigenvalues and singular values, and may serve as a basis for further investiga...

Constrained stress majorization is a promising new technique for integrating application specific layout constraints into forcedirected graph layout. We significantly improve the speed and convergence properties of the constrained stress-majorization technique for graph layout by employing a diagonal scaling of the stress function. Diagonal scaling requires the active-set quadratic programming ...