Lower bounds for the smallest singular value

Lower Bounds for the Smallest Singular Value of Structured Random Matrices

We obtain lower tail estimates for the smallest singular value of random matrices with independent but non-identically distributed entries. Specifically, we consider n× n matrices with complex entries of the form M = A ◦X +B = (aijξij + bij) where X = (ξij) has iid centered entries of unit variance and A and B are fixed matrices. In our main result we obtain polynomial bounds on the smallest si...

A Lower Bound for the Smallest Singular Value

In this paper, we obtain a lower bound for the smallest singular value of nonsingular matrices which is better than the bound presented by Yu and Gu [Linear Algebra Appl. 252(1997)25-38]. Meanwhile, we give some numerical examples which will show the effectiveness of our result.

A parameterized lower bound for the smallest singular value

This paper presents a parameterized lower bound for the smallest singular value of a matrix based on a new Geršgorin-type inclusion region that has been established recently by these authors. The comparison of the new lower bound with known ones is supplemented with a numerical example.

A Smallest Singular Value Method for Solving Inverse Eigenvalue Problems

Utilizing the properties of the smallest singular value of a matrix, we propose a new, efficient and reliable algorithm for solving nonsymmetric matrix inverse eigenvalue problems, and compare it with a known method. We also present numerical experiments which illustrate our results.

Loewner matrix ordering in estimation of the smallest singular value