Matrix completion via a low rank factorization model and an Augmented Lagrangean Succesive Overrelaxation Algorithm
Journal Title: Bulletin of Computational Applied Mathematics (Bull CompAMa) - Year 2014, Vol 2, Issue 2
Abstract
The matrix completion problem (MC) has been approximated by using the nuclear norm relaxation. Some algorithms based on this strategy require the computationally expensive singular value decomposition (SVD) at each iteration. One way to avoid SVD calculations is to use alternating methods, which pursue the completion through matrix factorization with a low rank condition. In this work an augmented Lagrangean-type alternating algorithm is proposed. The new algorithm uses duality information to define the iterations, in contrast to the solely primal LMaFit algorithm, which employs a Successive Over Relaxation scheme. The convergence result is studied. Some numerical experiments are given to compare numerical performance of both proposals.
Authors and Affiliations
Hugo Lara, Harry Oviedo, Jinjun Yuan
New results on the stability, integrability and boundedness in Volterra integro-differential equations
The authors of this article deal with a first order non-linear Volterra integro-differential equation (NVIDE). To this end, the conditions are obtained which are sufficient for stability (S), boundedness (B), and for eve...
The exponential distribution as the sum of discontinuous distributions
We show that for any natural number $n$, an exponential distribution can be written as the sum of $n$ discontinuous variables and another exponential distribution, all of them independent.
A deterministic optimization approach for solving the rainfall disaggregation problem
One of the main problems in hydrology is the time scale of the historical rainfall data, available from many meteorological data bases. Most of the rainfall data is given at a time scale coarser than the one needed for...
L(2,1)-Labeling for Subdivisions of Cycle Dominated Graphs
Let G(V,E) be a simple, finite, connected, undirected graph. Distance two labeling or L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of non-negative integers such that |f(x)-f(y)| &ge...
Fundamentals of soft category theory
The soft category theory offers a way to study soft theories developed so far more generally. The main purpose of this paper is to introduce the basic algebraic operations in soft categories, and for that we introduce so...