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Open AccessArticle

A Gradient System for Low Rank Matrix Completion

Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica (DISIM), Università dell’Aquila, via Vetoio 1, 67100 L’Aquila, Italy
Section of Mathematics, Gran Sasso Science Institute, via Crispi 7, 67100 L’Aquila, Italy
Author to whom correspondence should be addressed.
Axioms 2018, 7(3), 51;
Received: 7 May 2018 / Revised: 18 July 2018 / Accepted: 18 July 2018 / Published: 24 July 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix X to M, where the distance is measured in the Frobenius norm. A key element in the solution of this matrix nearness problem consists of the use of a constrained gradient system of matrix differential equations. The obtained results, compared to those obtained by different approaches show that the method has a correct behaviour and is competitive with the ones available in the literature. View Full-Text
Keywords: low rank completion; matrix ODEs; gradient system low rank completion; matrix ODEs; gradient system
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Scalone, C.; Guglielmi, N. A Gradient System for Low Rank Matrix Completion. Axioms 2018, 7, 51.

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