Related papers: A new improved error bound for linear complementar…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
We obtain a new bound in the uniform version of the Glasner property for matrices with polynomial entries, improving that of K. Bulinski and A. Fish (2021). This improvement is based on a more careful examination of complete rational…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
In this work we study approximation algorithms for the \textit{Bounded Color Matching} problem (a.k.a. Restricted Matching problem) which is defined as follows: given a graph in which each edge $e$ has a color $c_e$ and a profit $p_e \in…
This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a better convergence rate in more general cases, and 2) explicit…
In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and randomly distributed over a finite field. The decoding radius…
In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…
We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…
We present improved approximation bounds for the Moore-Penrose inverses of banded matrices, where the bandedness is induced by a metric on the index set. We show that the pseudoinverse of a banded matrix can be approximated by another…
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
In this paper, we discuss the perturbation analysis of the extended vertical linear complementarity problem (EVLCP). Under the assumption of the row $\mathcal{W}$-property, several absolute and relative perturbation bounds of EVLCP are…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
This study investigates the misclassification excess risk bound in the context of 1-bit matrix completion, a significant problem in machine learning involving the recovery of an unknown matrix from a limited subset of its entries. Matrix…
For many applications, it is convenient to have good upper bounds for the norm of the inverse of a given matrix. In this paper, we obtain such bounds when A is a Nekrasov matrix, by means of a scaling matrix transforming A into a strictly…
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…
Duan, Wu and Zhou (FOCS 2023) recently obtained the improved upper bound on the exponent of square matrix multiplication $\omega<2.3719$ by introducing a new approach to quantify and compensate the ``combination loss" in prior analyses of…
To our knowledge, the error and perturbation bounds of the general absolute value equations are not discussed. In order to fill in this study gap, in this paper, by introducing a class of absolute value functions, we study the error and…
Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…