Related papers: New permanent approximation inequalities via ident…
We present new identities for determinants of matrices $(A_{i,j})$ with entries $A_{i,j}$ equal to $a_{i,j}$ or $a_{i,0}a_{0,j}-a_{i,j}$, where the $a_{i,j}$'s are indeterminates. We show that these identities are behind trace identities…
We present a randomized approximation scheme for the permanent of a matrix with nonnegative entries. Our scheme extends a recursive rejection sampling method of Huber and Law (SODA 2008) by replacing the upper bound for the permanent with a…
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…
Consider $n$ linearly independent vectors in $\mathbb{C}^n$ which form columns of a matrix $A$. The recursive evaluation of eigen directions (normalized eigenvectors) of $A$ is the solution of an eigenvalue problem of the form…
This paper deals with two main topics related to Diophantine approximation. Firstly, we show that if a point on an algebraic variety is approximable by rational vectors to a sufficiently large degree, the approximating vectors must lie in…
We prove that uniform random triangulations whose genus is proportional to their size $n$ have diameter of order $\log n$ with high probability. We also show that in such triangulations, the distances between most pairs of points differ by…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…
We characterize ratios of permanents of (generalized) submatrices which are bounded on the set of all totally positive matrices. This provides a permanental analog of results of Fallat, Gekhtman, and Johnson [{\em Adv.\ Appl.\ Math.} {\bf…
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.
The aim of this manuscript is to derive bounds on the moduli of eigenvalues of special type of rational matrices of the form $T(\lambda) = \displaystyle -B_0 +I\lambda +\frac{B_1}{\lambda-\alpha_1}+ \dots+ \frac{B_m}{\lambda-\alpha_m}$,…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
Approximating solutions of ordinary and partial differential equations constitutes a significant challenge. Based on functional expressions that inherently depend on neural networks, neural forms are specifically designed to precisely…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We demonstrate $k+1$-term arithmetic progressions in certain subsets of the real line whose "higher-order Fourier dimension" is sufficiently close to 1. This Fourier dimension, introduced in previous work, is a higher-order (in the sense of…
This work develops new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal number of generators to measure the size of codes. We prove a…