相关论文: An Efficient Algorithm for Latin Squares in a Bipa…

We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…

This article, showing that almost all objects in the title are asymmetric, is re-typed from a manuscript I wrote somewhere around 1980 (after the papers of Bang and Friedland on the permanent conjecture but before those of Egorychev and…

This paper presents the applications of Eigenvalues and Eigenvectors (as part of spectral decomposition) to analyze the bipartivity index of graphs as well as to predict the set of vertices that will constitute the two partitions of graphs…

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…

Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this…

We investigate the space complexity of solving linear systems of equations. While all known deterministic or randomized algorithms solving a square system of $n$ linear equations in $n$ variables require $\Omega(\log^2 n)$ space, Ta-Shma…

The Bethe-Salpeter eigenvalue problem is a structured eigenvalue problem arising in many-body physics. In practice, a few of the smallest positive eigenvalues and the corresponding eigenvectors need to be computed. In principle, the LOBPCG…

This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computing eigenvalues located inside a given disk, and the proposed…

We consider min-max optimization problems for polynomial functions, where a multivariate polynomial is maximized with respect to a subset of variables, and the resulting maximal value is minimized with respect to the remaining variables.…

We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which which suggests…

We consider a problem in eigenvalue optimization, in particular finding a local minimizer of the spectral abscissa - the value of a parameter that results in the smallest value of the largest real part of the spectrum of a matrix system.…

In 2008, Cavenagh and Dr\'{a}pal, et al, described a method of constructing Latin trades using groups. The Latin trades that arise from this construction are entry-transitive (that is, there always exists an autoparatopism of the Latin…

This paper is a continuation of \ct{cmf16} where an efficient algorithm for computing the maximal eigenpair was introduced first for tridiagonal matrices and then extended to the irreducible matrices with nonnegative off-diagonal elements.…

We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…

Various physical models can be expressed in terms of matrices. A valuable tool for analysing matrix models is numerical simulations, often the Metropolis algorithm with various improvements. The downside of this approach is that the…

We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where…

We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…

The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…

We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The…

The LATIN method has been developed and successfully applied to a variety of deterministic problems, but few work has been developed for nonlinear stochastic problems. This paper presents a stochastic LATIN method to solve stochastic and/or…