Related papers: Solving the problem of simultaneous diagonalizatio…
We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…
A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such…
In this paper a geometric method based on Grassmann manifolds and matrix Riccati equations to make hermitian matrices diagonal is presented. We call it Riccati Diagonalization.
We establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…
A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which…
We prove that the range of a symmetric matrix over F_2 contains the vector of its diagonal elements. We apply the theorem to a generalization of the "Lights Out" problem on graphs.
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their…
We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including H\"olderian growth…
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
We revisit the matrix problems sparse null space and matrix sparsification, and show that they are equivalent. We then proceed to seek algorithms for these problems: We prove the hardness of approximation of these problems, and also give a…
This paper investigates scalable frame in ${\mathbb R}^n$. We define the reduced diagram matrix of a frame and use it to classify scalability of the frame under some conditions. We give a new approach to the scaling problem by breaking the…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and…
Partitioning sparse matrices and graphs is a common and important problem in many scientific and graph analytics applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as…