A Gradient System for Low Rank Matrix Completion
by
Carmela Scalone 1,* and Nicola Guglielmi 2
Carmela Scalone 1,* and Nicola Guglielmi 2
1
Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica (DISIM), Università dell’Aquila, via Vetoio 1, 67100 L’Aquila, Italy
2
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; https://doi.org/10.3390/axioms7030051
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.
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Keywords:
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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