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The CP-Matrix Completion Problem [PDF]
SIAM Journal on Matrix Analysis and Applications, 2014 A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C=BB^T$. The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix (i.e., a matrix having unknown entries) such that the completed matrix is completely positive.
An-Wa Zhou, Jinyan Fan
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Linear Algebra and Its Applications, 2003 An \(n \times n\) matrix is called an \(N\)-matrix if all principal minors are negative. The authors prove that a combinatorially symmetric partial \(N\)-matrix has an \(N\)-matrix completion if the graph of its specified entries is a 1-chordal graph.
Ana M Urbano +2 more
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The Euclidian Distance Matrix Completion Problem
SIAM Journal on Matrix Analysis and Applications, 1995Motivated by the molecular conformation problem, completions of partial Euclidian distance matrices are studied. It is proved that any partial distance matrix with a chordal graph can be completed to a distance matrix. Given any nonchordal graph G, it is shown that there is a partial distance matrix A with graph G such that A does not admit any ...
Charles R Johnson, Mihály Bakonyi
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The Symmetric N-Matrix Completion Problem
Linear Algebra and Its Applications, 2005 A real \(n\times n\) matrix is called an \(N\)-matrix if all its principal minors are negative. Consider a partial symmetric matrix \(A\) where some entries are unspecified. The problem under consideration is whether it is possible to determine these unspecified entries in such a way that the resulting fully specified symmetric matrix is an \(N ...
Ana M Urbano +2 more
exaly +2 more sources
On a Class of Matrix Completion Problems
Mathematische Nachrichten, 1989The paper contains a unified treatment of special classes of matrix extension problems (``Schur analysis''). It is characterized as a combination of methods developed by V. P. Potapov and his collaborators in the study of the so-called fundamental matrix inequalities and of methods used by the last two authors.
Dubovoj, Vladimir K. +2 more
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The positive Q-matrix completion problem
Discrete Mathematics, Algorithms and Applications, 2015A real [Formula: see text] matrix is a [Formula: see text]-matrix if for [Formula: see text] the sum of all [Formula: see text] principal minors is positive. A digraph [Formula: see text] is said to have positive [Formula: see text]-completion if every partial positive [Formula: see text]-matrix specifying [Formula: see text] can be completed to a ...
Bhaba Kumar Sarma, Kalyan Sinha
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