Related papers: Maximum determinant positive definite Toeplitz com…

We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a…

This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of…

A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant. The problem of detecting their copositivity is NP-hard.…

We examine the problem of approximating a positive, semidefinite matrix $\Sigma$ by a dyad $xx^T$, with a penalty on the cardinality of the vector $x$. This problem arises in sparse principal component analysis, where a decomposition of…

This paper addresses the challenge of Toeplitz covariance matrix estimation from partial entries of random quantized samples. To balance trade-offs among the number of samples, the number of entries observed per sample, and the data…

We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the…

We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…

A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…

We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to…

Motivated by recent works on statistics of matrices over sets of number theoretic interest, we study matrices with entries from arbitrary finite subsets $\mathcal A$ of finite rank multiplicative groups infields of characteristic zero. We…

A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal.…

A new method of analysing positive bistochastic maps on the algebra of complex matrices $M_{3}$ has been proposed. By identifying the set of such maps with a convex set of linear operators on $\mathbb{R}^{8}$, one can employ techniques from…

We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…

Toeplitz matrices are characterized by their constant diagonals, have been extensively studied in various settings, including over real and complex numbers. However, their study over quaternions is quite sparse. In this paper, we…

We propose a method for verifying that a given feasible point for a polynomial optimization problem is globally optimal. The approach relies on the Lasserre hierarchy and the result of Lasserre regarding the importance of the convexity of…

We give an easy proof to show that every complex normal Toeplitz matrix is classified as either of type I or of type II. Instead of difference equations on elements in the matrix used in past studies, polynomial equations with coefficients…

We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…

We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable $X$. This algorithm rests on the factorization $X=Y Y^T$, where the number of columns of Y fixes the rank of…

We consider the multi-view data completion problem, i.e., to complete a matrix $\mathbf{U}=[\mathbf{U}_1|\mathbf{U}_2]$ where the ranks of $\mathbf{U},\mathbf{U}_1$, and $\mathbf{U}_2$ are given. In particular, we investigate the…

We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of…