Related papers: Computing nearest stable matrix pairs
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
We propose an alternative definition for families of stable pairs $(X,D)$ over a possibly non-reduced base when $D$ is reduced, by replacing $(X,D)$ with an appropriate orbifold pair $(\mathcal X,\mathcal D)$. This definition of a stable…
In recent years, there has been a considerable amount of interest in stability of equations and their corresponding groups. Here, we initiate the systematic study of the quantitative aspect of this theory. We develop a novel method,…
We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable…
We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of exchangeable pairs for multivariate normal…
Consider a matrix polynomial $P \left( \lambda \right)= A_0 + \lambda A_1 + \ldots + \lambda^d A_d$, with $A_0,\ldots, A_d$ complex (or real) matrices with a certain structure. In this paper we discuss an iterative method to numerically…
We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where both differentiability and nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of…
We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input…
We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair $(A,B)$ we provide a normal form with a minimal number of independent parameters to which all pairs of…
In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt{s}} \quad {\rm for\ all} \ {\bf x},$$ where ${\bf…
This letter proposes a mass-matrix differential-algebraic equation (DAE) formulation for transient stability simulation. This formulation has two prominent advantages: compatible with a multitude of implicit DAE solvers and can be…
Consider $n \times n$ matrix $A$ and a set $\Lambda$ consisting of $k \le n$ prescribed complex numbers. Lippert (2010) in a challenging article, studied geometrically the spectral norm distance from $A$ to the set $\Lambda$ and constructed…
This paper considers the problem of finding the nearest $\Omega$-stable pencil to a given square pencil $A+xB \in \mathbb{C}^{n \times n}$, where a pencil is called $\Omega$-stable if it is regular and all of its eigenvalues belong to the…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
In this paper, we propose a way to combine two acceleration techniques for the $\ell\_{1}$-regularized least squares problem: safe screening tests, which allow to eliminate useless dictionary atoms; and the use of fast structured…
Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well…