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THE QMATRIX COMPLETION PROBLEM
, 2009
"... A real n × n matrix is a Qmatrix if for every k =1, 2,...,n the sum of all k × k principal minors is positive. A digraph D is said to have Qcompletion if every partial Qmatrix specifying D can be completed to a Qmatrix. For the Qcompletion problem, sufficient conditions for a digraph to have Q ..."
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A real n × n matrix is a Qmatrix if for every k =1, 2,...,n the sum of all k × k principal minors is positive. A digraph D is said to have Qcompletion if every partial Qmatrix specifying D can be completed to a Qmatrix. For the Qcompletion problem, sufficient conditions for a digraph to have
1 Introduction to the Matrix Completion Problem
, 2013
"... This is sometimes called the Netflix problem. A motivation for the matrix completion problem comes from user ratings of some products which are put into a matrix M. The entries Mij of the matrix correspond to the j’th user’s rating of product i. We assume that there exists an ideal ..."
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This is sometimes called the Netflix problem. A motivation for the matrix completion problem comes from user ratings of some products which are put into a matrix M. The entries Mij of the matrix correspond to the j’th user’s rating of product i. We assume that there exists an ideal
A survey on the matrix completion problem
 Trends in Mathematics
"... Abstract. Completion problems arise in a variety of applications, such as statistics (e.g. entropy methods for missing data), chemistry (the molecular conformation problem), systems theory, discrete optimization (relaxation methods), data compression, etc., as well as in operator theory and within ..."
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Cited by 1 (0 self)
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matrix theory (e.g. determinantal inequalities). In addition to applications, completion problems have provided an excellent mechanism for understanding matrix structure more deeply. In this article, we survey the recent works on matrix completion problems. 1.
The P0matrix completion problem
 Electronic Journal of Linear Algebra
"... Abstract. In this paper the P0matrix completion problem is considered. It is established that every asymmetric partial P0matrix has P0completion. All 4 × 4 patterns that include all diagonal positions are classified as either having P0completion or not having P0completion. It is shown that any ..."
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Cited by 6 (3 self)
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Abstract. In this paper the P0matrix completion problem is considered. It is established that every asymmetric partial P0matrix has P0completion. All 4 × 4 patterns that include all diagonal positions are classified as either having P0completion or not having P0completion. It is shown that any
Graph Theoretic Methods for Matrix Completion Problems
 Linear Algebra Appl
"... A pattern is a list of positions in an n n real matrix. A matrix completion problem for the class of Pmatrices asks whether every partial Pmatrix whose specified entries are exactly the positions of the pattern can be completed to a Pmatrix. We survey the current state of research on Pmatrix c ..."
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Cited by 31 (10 self)
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A pattern is a list of positions in an n n real matrix. A matrix completion problem for the class of Pmatrices asks whether every partial Pmatrix whose specified entries are exactly the positions of the pattern can be completed to a Pmatrix. We survey the current state of research on Pmatrix
Douglas–Rachford Feasibility Methods for Matrix Completion Problems ∗
, 2013
"... In this paper we give general recommendations for successful application of the Douglas–Rachford reflection method to convex and nonconvex real matrixcompletion problems. These guidelines are demonstrated by various illustrative examples. ..."
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Cited by 3 (2 self)
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In this paper we give general recommendations for successful application of the Douglas–Rachford reflection method to convex and nonconvex real matrixcompletion problems. These guidelines are demonstrated by various illustrative examples.
THE N 1 0MATRIX COMPLETION PROBLEM
"... Abstract. An n × n matrix is called an N 1 0matrix if all its principal minors are nonpositive and each entry is nonpositive. In this paper, we study general combinatorially symmetric partial N 1 0matrix completion problems and prove that a combinatorially symmetric partial N 1 0matrix with all ..."
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Abstract. An n × n matrix is called an N 1 0matrix if all its principal minors are nonpositive and each entry is nonpositive. In this paper, we study general combinatorially symmetric partial N 1 0matrix completion problems and prove that a combinatorially symmetric partial N 1 0matrix
THE N 1 0MATRIX COMPLETION PROBLEM
"... Abstract. An n × n matrix is called an N 1 0matrix if all its principal minors are nonpositive and each entry is nonpositive. In this paper, we study general combinatorially symmetric partial N 1 0matrix completion problems and prove that a combinatorially symmetric partial N 1 0matrix with all ..."
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Abstract. An n × n matrix is called an N 1 0matrix if all its principal minors are nonpositive and each entry is nonpositive. In this paper, we study general combinatorially symmetric partial N 1 0matrix completion problems and prove that a combinatorially symmetric partial N 1 0matrix
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