Related papers: Two new lower bounds for the smallest singular val…
We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are…
Lower bounds for some explicit decision problems over the complex numbers are given.
This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic…
A proof for the lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes. The bound has a similar form as the one by Graham and McLean [SIAM J. Numer. Anal., 44 (2006), pp.…
A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in [C.Q. Li et al., A new error bound for linear complementarity problems for B-matrices.…
This paper deals with the numerical computation of the least singular value of a rectangular matrix $A$ relative to a pair of closed convex cones $(P,Q)$, which is defined as the optimal value of the non-convex optimization problem of…
In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…
We apply Tatuzawa's version of Siegel's theorem to derive two lower bounds on the size of the principal genus of positive definite binary quadratic forms.
Using an approach of Bergh, we give an alternate proof of Bennett's result on lower bounds for non-negative matrices acting on non-increasing non-negative sequences in $l^p$ when $p \geq 1$ and its dual version, the upper bounds when $0<p…
New error bounds for the linear complementarity problems are given respectively when the involved matrices are Nekrasov matrices and B-Nekrasov matrices. Numerical examples are given to show that new bounds are better respectively than…
This paper concerns singular value decomposition (SVD)-based computable formulas and bounds for the condition number of the Total Least Squares (TLS) problem. For the TLS problem with the coefficient matrix $A$ and the right-hand side $b$,…
Let $M_n$ be an $n$ by $n$ random matrix where each entry is +1 or -1 independently with probability 1/2. Our main result implies that the probability that $M_n$ is singular is at most $(1/\sqrt{2} + o(1))^n$, improving on the previous best…
In this paper, we establish a lower bound on the level of a perfect complex with power torsion homology on positive degrees and a power torsion minimal generator for zero homology. Examples are provided to demonstrate that the bound is…
We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.
This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…
Let $\a$ be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of $\a$ and $M$ be a fixed matrix of the same size. The goal of this paper is to give a…
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…
We prove two basic conjectures on the distribution of the smallest singular value of random n times n matrices with independent entries. Under minimal moment assumptions, we show that the smallest singular value is of order n^{-1/2}, which…
We prove a lower bound on the dimension of the set of maximal border subrank tensors. This is the first such bound of its type.