Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique

Computing the Nearest Correlation Matrix

Computing the Nearest Rank-Deficient Matrix Polynomial

Matrix polynomials appear in many areas of computational algebra, control systems theory, di‚erential equations, and mechanics, typically with real or complex coecients. Because of numerical error and instability, a matrix polynomial may appear of considerably higher rank (generically full rank), while being very close to a rank-de€cient matrix. “Close” is de€ned naturally under the Frobenius ...

Approximation of rank function and its application to the nearest low-rank correlation matrix

The rank function rank(·) is neither continuous nor convex which brings much difficulty to the solution of rank minimization problems. In this paper, we provide a unified framework to construct the approximation functions of rank(·), and study their favorable properties. Particularly, with two families of approximation functions, we propose a convex relaxation method for the rank minimization p...

Optimized projections for compressed sensing via rank-constrained nearest correlation matrix

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper a novel formulation of the optimization problem is proposed, in the form of a rank-constrained nearest correlation matrix problem. Furthermore, improvements ...

A Sequential Semismooth Newton Method for the Nearest Low-rank Correlation Matrix Problem

Based on the well-known result that the sum of the largest eigenvalues of a symmetric matrix can be represented as a semidefinite programming problem (SDP), we formulate the nearest low-rank correlation matrix problem as a nonconvex SDP and propose a numerical method that solves a sequence of least-square problems. Each of the least-square problems can be solved by a specifically designed semis...