Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical numerical perspectives. Namely, we show convergence the method establish properties couple majorization approaches for associated problems. also test monotone al...

Euclidean distance matrices (EDM) are symmetric nonnegative with several interesting properties. In this article, we introduce a wider class of called generalized (GEDMs) that include EDMs. Each GEDM is an entry-wise matrix. A not unless it EDM. By some new techniques, show many significant results on can be extended to matrices. These contain about eigenvalues, inverse, determinant, spectral r...

In this paper, we consider the joint design of source precoding matrix and the relay precoding matrix in a two-hop multiple-input multiple-output relay network. The goal is to find a pair of matrices in order to minimize the power consumption and at the same time meet pre-selected quality of service constraints that are defined as the mean square error of each data stream. Using majorization th...

It is convenient to define H(X) = Hα(X) = −∞ when X is discrete, e.g., degenerate. (Our notation differs from that of Karlin and Rinott 1981 here.) We study the entropy of a weighted sum, S = ∑n i=1 aiXi, of i.i.d. random variables Xi, assuming that the density f of Xi is log-concave, i.e., supp(f) = {x : f(x) > 0} is an interval and log f is a concave function on supp(f). The main result is th...

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 ...

We present a fundamentally different approach to orthogonal layout of data flow diagrams with ports. This is based on extending constrained stress majorization to cater for ports and flow layout. Because we are minimizing stress we are able to better display global structure, as measured by several criteria such as stress, edge-length variance, and aspect ratio. Compared to the layered approach...

In this series of papers we study subspaces of de Branges spaces of entire functions which are generated by majorization on subsets D of the closed upper half-plane. The present, first, part is addressed to the question which subspaces of a given de Branges space can be represented by means of majorization. Results depend on the set D where majorization is permitted. Significantly different sit...

We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected ...