The positive definite completion problem relative to a subspace

The Positive Definite Matrix Completion Problem: an Optimization Viewpoint∗

We look at the real positive (semi)definite matrix completion problem from the relative entropy minimization viewpoint. After the problem is transformed into the standard maxdet from, conditions are sought for existence of positive (semi)definite completions. Using basic tools of convex analysis results previously established using graph-theoretic or functional-analytic techniques are recovered...

Active Positive-Definite Matrix Completion

In the FindCandidates function (line 4), Select finds all the single edges that can be added to the current mask graph GΩ while maintaining its chordal structure. To do that, we make use of the clique tree data structure as introduced by Ibarra [1]. Given a graph G = (V,E), the clique tree is a tree C = (VC , EC), in which each node is a maximal clique of G, i.e., VC ⊂ 2 . In our case the numbe...

POSITIVE DEFINITE COMPLETION PROBLEMS FOR DIRECTED ACYCLIC GRAPHS By

A positive definite completion problem pertains to determining whether the unspecified positions of a partial (or incomplete) matrix can be completed in a desired subclass of positive definite matrices. In this paper we study an important and new class of positive definite completion problems where the desired subclasses are the spaces of covariance and inverse-covariance matrices of probabilis...

A New Algorithm for the Positive Semi-definite Procrustes Problem

For arbitrary real matrices F and G, the positive semi-deenite Procrustes problem is minimization of the Frr obenius norm of F ? PG with respect to positive semi-deenite symmetric P. Existing solution algorithms are based on a convex programming approach. Here an unconstrained non-convex approach is taken, namely writing P = E 0 E and optimizing with respect to E. The main result is that all lo...

Schoenberg’s Problem on Positive Definite Functions