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Inverse M-Matrix Completion Problem With Zeros in the Inverse Completion
A partially specified matrix \(A\) is said to be combinatorially symmetric if \(a_{ij}\) is specified if and only if \(a_{ji}\) is specified. The completion problem considered is to find the unspecified elements such that its completion is the inverse of an \(M\)-matrix. In the combinatorially symmetric case, this was solved by \textit{C. R.
Cristina Jordán
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Matrix completion problems in multidimensional systems
ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349), 2003A ring with identity is Hermite if every unimodular row vector over the ring can be completed to form a unimodular square matrix over the ring. This paper constructs examples and counter-examples of Hermite rings and formulates several open problems, which have potential applications in multidimensional systems.
Lawton, Wayne M., Lin, Zhiping
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A Note on Matrix Completion Problems
Algebra Colloquium, 2012Matrix completion problems are an important subclass of problems in matrix theory. An important question in matrix completion problems was posed by Oliveira in 1975, where the author proposed the description of the characteristic polynomial of a partitioned matrix of the form A = [Ai,j], i, j ∈ {1,2} (whose entries are in a field and A1,1, A2,2 are ...
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State covariances and the matrix completion problem
52nd IEEE Conference on Decision and Control, 2013State statistics of a linear system obey certain structural constraints that arise from the underlying dynamics and the directionality of input disturbances. Herein, we formulate completion problems of partially known state statistics with the added freedom of identifying disturbance dynamics.
Yongxin Chen 0002 +2 more
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2000
In the matrix completion problem we are given a partial symmetric real matrix A with certain elements specified or fixed and the rest are unspecified or free; and, we are asked whether A can be completed to satisfy a given property (P) by assigning certain values to its free elements.
Abdo Alfakih, Henry Wolkowicz
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In the matrix completion problem we are given a partial symmetric real matrix A with certain elements specified or fixed and the rest are unspecified or free; and, we are asked whether A can be completed to satisfy a given property (P) by assigning certain values to its free elements.
Abdo Alfakih, Henry Wolkowicz
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Euclidean distance matrix completion problems
Optimization Methods and Software, 2012Our experiments show that the method easily solves the artificial problems introduced by More and Wu. It also solves the 12 much more difficult protein fragment problems introduced by Hendrickson, and the six larger protein problems introduced by Grooms, Lewis and Trosset.
Haw-ren Fang, Dianne P. O'Leary
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A Matrix Completion Approach to Linear Index Coding Problem [PDF]
In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding problem is devised in order to find the optimum transmission rate given vector length and size of the field.
Babak Hassibi, Farshad Lahouti
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Randomized Robust matrix Completion for the Community Detection Problem
2018 52nd Asilomar Conference on Signals, Systems, and Computers, 2018This paper focuses on the unsupervised clustering of large partially observed graphs. We propose a provable randomized framework in which a clustering algorithm is applied to a graph’s adjacency matrix generated from a stochastic block model. A sub-matrix is constructed using random sampling, and the low rank component is found using a convex ...
Adel Karimian +3 more
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The General Matrix Pencil Completion Problem: A Minimal Case
SIAM Journal on Matrix Analysis and Applications, 2019In this paper we resolve a classical, long-standing open general matrix pencil completion problem in a minimal case. The problem consists of describing the possible Kronecker invariants of a pencil with a prescribed subpencil, and the restriction we impose is not structural but is only on the number of added rows and columns.
Marija Dodig, Marko Stosic
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Matrix decomposition problem is complete for the average case
Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, 2002The first algebraic average-case complete problem is presented. The focus of attention is the modular group, i.e., the multiplicative group SL/sub 2/(Z) of two-by-two integer matrices of determinant 1. By default, in this study matrices are elements of the modular group. The problem is arguably the simplest natural average-case complete problem to date.
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