Related papers: The Minimum-Rank Gram Matrix Completion via Modifi…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…

The FC-Gram algorithm approximates non-periodic functions to high order by constructing a periodic extension with controlled boundary behavior and applying trigonometric interpolation. In this paper we introduce a generalized FC-Gram…

In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…

This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…

We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…

This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe…

Let $f,g_1,\dots,g_m$ be polynomials with real coefficients in a vector of variables $x=(x_1,\dots,x_n)$. Denote by $\text{diag}(g)$ the diagonal matrix with coefficients $g=(g_1,\dots,g_m)$ and denote by $\nabla g$ the Jacobian of $g$. Let…

This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…

We propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

We exploit the versatile framework of Riemannian optimization on quotient manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank matrix completion. The underlying search space of fixed-rank matrices is endowed with a…

We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…

In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a…

This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…

We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…

We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…

We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the Bernstein basis; it can be seen as generalization of the…