相关论文: Weighted matrix means and symmetrization procedure…
Weighted bipolar argumentation frameworks offer a tool for decision support and social media analysis. Arguments are evaluated by an iterative procedure that takes initial weights and attack and support relations into account. Until…
A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph.…
In this paper, the Mean value iterative process is modified with the Mann iterative process for mean nonexpansive mapping in a hyperbolic metric space that satisfy the symmetry criteria and in uniformly convex hyperbolic spaces to validate…
A generalized word in two positive definite matrices A and B is a finite product of nonzero real powers of A and B. Symmetric words in positive definite A and B are positive definite, and so for fxed B, we can view a symmetric word, S(A,B),…
We develop a comprehensive theory for a general class of multi-parameter function spaces of Besov-Triebel-Lizorkin type, with a matrix weight. We prove the equivalence of different quasi-norms, the identification of function and sequence…
We establish a weighted simultaneous Khintchine-type theorem, both convergence and divergence, for all nondegenerate manifolds, which answers a problem posed in [Math. Ann., 337(4):769-796, 2007]. This extends the main results of [Acta…
On the space of positive definite matrices we consider distance functions of the form $d(A,B)=\left[\tr\mathcal{A}(A,B)-\tr\mathcal{G}(A,B)\right]^{1/2},$ where $\mathcal{A}(A,B)$ is the arithmetic mean and $\mathcal{G}(A,B)$ is one of the…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, with as few matrix-matrix multiplications as possible. More precisely, let $\Pi_{2^{m}}^*$ represent the set of polynomials computable with…
We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their…
In this work we classify all the order-two Hypergeometric operators $D$, symmetric with respect to some $2\times 2$ irreducible matrix-weight $W$ such that $DP_n=P_n\left(\begin{smallmatrix} \lambda_n&0\\0&\mu_n \end{smallmatrix} \right)$…
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…
We settle an open problem of several years standing by showing that the least-squares mean for positive definite matrices is monotone for the usual (Loewner) order. Indeed we show this is a special case of its appropriate generalization to…
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on $\mathbb{R}^n$. Rearrangements are maps that are monotonic (up to sets of measure zero) and…
The weighted projection of an alternating sign matrix (ASM) was introduced by Brualdi and Dahl (2018) as a step towards characterising a generalisation of Latin squares they introduced using alternating sign hypermatrices. If $z_n =…
We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer…
The long run behaviour of linear dynamical systems is often studied by looking at eventual properties of matrices and recurrences that underlie the system. A basic problem that lies at the core of many questions in this setting is the…
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to…
We show how up-to techniques for (bi-)similarity can be used in the setting of weighted systems. The problems we consider are language equivalence, language inclusion and the threshold problem (also known as universality problem) for…
This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive…