Related papers: A new solution to square matrix completion problem
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can…
A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C=BB^T$. The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix (i.e.,…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9,…
We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of authors' knowledge, there exists merely one efficient algorithm…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
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)…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
Euler had considered the problem of finding three integers whose sum, product, and also the sum of the products of the integers, taken two at a time, are all perfect squares. Euler's methods of solving the problem lead to parametric…
Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split…
Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized…