Related papers: Projecting onto rectangular matrices with prescrib…
Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently,…
The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of characterizing the instances where such an equality holds.…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points. To compute (with) the 0-dimensional projection and the…
The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
Random Projections have been widely used to generate embeddings for various graph learning tasks due to their computational efficiency. The majority of applications have been justified through the Johnson-Lindenstrauss Lemma. In this paper,…
Tomography is the area of reconstructing objects from projections. Here we wish to reconstruct a set of cells in a two dimensional grid, given the number of cells in every row and column. The set is required to be an hv-convex polyomino,…
We characterize the existence of a polynomial (rational) matrix when its eigenstructure (complete structural data) and some of its rows are prescribed. For polynomial matrices, this problem was solved in a previous work when the polynomial…
A comprehensive approach for real-time computations using a database of parameterized linear reduced-order models (ROMs) is proposed. The method proceeds by sampling offline ROMs for specific values of the parameters and interpolating…
We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…
The main goal of this paper is to give a general method to compute (via computer algebra systems) an explicit set of generators of the ideals of the projective embeddings of some ruled surfaces, namely projective line bundles over curves…
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of…
Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions. As…
We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of…
In contrast to conjunctions of commutable projection operators unambiguously represented by their meets, the mathematical representation of conjunctions of incommutable projection operators is a question that has yet to be solved. This…