Related papers: Matrix representations of multivalued projections …
Networks are structures that encode relationships between pairs of elements or nodes. However, there is no imposed connection between these relationships, i.e., the relationship between two nodes can be independent of every other one in the…
In analogy with the geometric situation, we study real calculi over projective modules and show that they can be realized as projections of free real calculi. Moreover, we consider real calculi over matrix algebras and discuss several…
We study the L1 minimization problem with additional box constraints. We motivate the problem with two different views of optimality considerations. We look into imposing such constraints in projected gradient techniques and propose a worst…
The equivalence of multidimensional systems is closely related to the reduction of multivariate polynomial matrices, with the Smith normal form of matrices playing a key role. So far, the problem of reducing multivariate polynomial matrices…
In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…
Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weak…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…
We discuss representations of the projective line over a ring $R$ with 1 in a projective space over some (not necessarily commutative) field $K$. Such a representation is based upon a $(K,R)$-bimodule $U$. The points of the projective line…
In this article, we express solutions of the Gauss hypergeometric equation as a series of the multiple polylogarithms by using iterated integral. This representation is the most simple case of a semisimple representation of solutions of the…
Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor…
In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…
In this work, we study the matrix representation of derivations for Mock-Lie algebras with dimensions up to four. Using matrix methods, we examine their structure and properties, showing how these derivations help us better understand the…
For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory…
A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective…
We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…