The positive definite matrix completion problem
نویسندگان
چکیده
منابع مشابه
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...
متن کاملActive 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...
متن کاملMinimizing the condition number of a positive definite matrix by completion
We consider the problem of minimizing the spectral condition number of a positive definite matrix by completion: min{cond( [ A BH B X ] ) : [ A BH B X ] positive definite}, where A is an n × n Hermitian positive definite matrix, B a p × n matrix and X is a free p× p Hermitian matrix. We reduce this problem to an optimization problem for a convex function in one variable. Using the minimal solut...
متن کاملThe Q-matrix completion problem
Abstract. A real n × n matrix is a Q-matrix if for every k = 1, 2, . . . , n the sum of all k × k principal minors is positive. A digraph D is said to have Q-completion if every partial Q-matrix specifying D can be completed to a Q-matrix. For the Q-completion problem, sufficient conditions for a digraph to have Q-completion are given, necessary conditions for a digraph to have Q-completion are...
متن کاملThe Nonsingular Matrix Completion Problem
An n × n matrix is called a principally nonsingular matrix (NSmatrix) if all its principal minors are different from zero and it is called a totally nonsingular matrix (TNS-matrix) if all its minors are different from zero. In this paper, we are interested in the NS-matrix (TNSmatrix) completion problem: whether a partial NS-matrix (TNS-matrix) has a NS-matrix (TNS-matrix) completion. Here, we ...
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ژورنال
عنوان ژورنال: Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie
سال: 2015
ISSN: 2222-4173,0254-3486
DOI: 10.4102/satnt.v34i1.1322