Related papers: Projecting onto rectangular matrices with prescrib…
The study of the combinatorial diameter of a polyhedron is a classical topic in linear-programming theory due to its close connection with the possibility of a polynomial simplex-method pivot rule. The 2-sum operation is a classical…
The paper proposes to decode Reed-Muller (RM) codes by projecting onto only a few subspaces such that the number of projections is significantly reduced. It reveals that the probability that error pairs are canceled simultaneously in two…
The row (column) completion problem of polynomial matrices of given degree with prescribed eigenstructure has been studied in \cite{AmBaMaRo23}, where several results of prescription of some of the four types of invariants that form the…
We consider generalized inverses of linear operators on arbitrary vector spaces and study the question when their product in reverse order is again a generalized inverse. This problem is equivalent to the question when the product of two…
The well-known M-P (Moore-Penrose) pseudoinverse is used in several linear-algebra applications; for example, to compute least-squares solutions of inconsistent systems of linear equations. It is uniquely characterized by four properties,…
In this note, we provide explicit expressions for the projections onto the graph of a quadratic polynomial. The projections are obtained by examining the critical points of the associated quartic polynomial, that is, the roots of the cubic…
Gale and Ryser found a criterion for existence of a binary matrix with given row and column sums. Mirsky extended the theorem of Gale and Ryser to $q$-ary matrices. In this paper, we are interested in higher dimensional extension of these…
We are presenting a method of linear regression based on Gram-Schmidt orthogonal projection that does not compute a pseudo-inverse matrix. This is useful when we want to make several regressions with random data vectors for simulation…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…
Typical template-based object pose pipelines estimate the pose by retrieving the closest matching template and aligning it with the observed image. However, failure to retrieve the correct template often leads to inaccurate pose…
Let $k$ and $i_1,\ldots,i_n$ be natural numbers. Place $k$ balls into a multidimensional box of $i_1\times\cdots \times i_n$ cells, no more than one ball to each cell, such that the projections to each of the coordinate axes have…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
We study the row completion problem of polynomial and rational matrices with partial prescription of the structural data. The prescription of the complete structural data has been solved in Amparan et al., Lin. Alg. Appl. 720 (2025)…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…
We derive a closed-form expression for the projection onto a capped rotated second-order cone -- a convex set that arises in perspective relaxations of nonlinear programs with binary indicator variables. The closed-form solution involves…
In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…
In this paper, we first establish a formula for exactly computing the regular coderivative of the metric projection operator onto closed balls $r\mathbb{B}$ centered at the origin in Hilbert spaces. Then, this result is extended to metric…
The block-iterative projections (BIP) method of Aharoni and Censor [Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, Linear Algebra and its Applications 120, (1989), 165--175] is an…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…