Related papers: Computing Nearby Non-trivial Smith Forms
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
In this paper, we prove that the Max-Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch. We describe two different approximation algorithms for the Max-Morse Matching Problem. For…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…
Quadratically optimized polynomials are described which are useful in multi-bosonic algorithms for Monte Carlo simulations of quantum field theories with fermions. Algorithms for the computation of the coefficients and roots of these…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
We explore computational aspects of maximum likelihood estimation of the mixture proportions of a nonparametric finite mixture model -- a convex optimization problem with old roots in statistics and a key member of the modern data analysis…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Finding the $r\times r$ submatrix of maximum volume of a matrix $A\in\mathbb R^{n\times n}$ is an NP hard problem that arises in a variety of applications. We propose a new greedy algorithm of cost $\mathcal O(n)$, for the case $A$…
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explicitly computed. We first show that this proximity operator…
In distributed optimization or Nash-equilibrium seeking over directed graphs, it is crucial to find a matrix norm under which the disagreement of individual agents' states contracts. In existing results, the matrix norm is usually defined…
We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…