We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive de nite matrix A. The factorization is not based on the Cholesky algorithm (or Gaussian elimination), but on A-orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modi cation. When used in conjunction with the conjugate gradient a...

SUMMARY We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive deenite matrix A. The factorization is not based on the Cholesky algorithm (or Gaussian elimination), but on A{orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modiication. When used in conjunction with the conjugate gr...

Tensor factorization arises in many machinelearning applications, such knowledge basemodeling and parameter estimation in latentvariable models. However, numerical meth-ods for tensor factorization have not reachedthe level of maturity of matrix factorizationmethods. In this paper, we propose a newmethod for CP tensor factorization that usesrandom projections to ...

The non-negative matrix factorization (NMF) algorithm is a classical matrix factorization and dimension reduction method in machine learning and data mining. However, in real problems, we always have to run the algorithm for several times and use the best matrix factorization result as the final output because of the random initialization of the matrix factorization. In this paper, we proposed ...

In this paper we discuss the parallel implementation of the Cholesky factorization of a positive definite symmetric matrix when that matrix is block tridiagonal. While parallel implementations for this problem, and closely related problems like the factorization of banded matrices, have been previously reported in the literature, those implementations dealt with the special cases where the bloc...

Recently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions, under which an oscillatory tetradiagonal matrix can have such Oscillatory Toeplitz are examined as case study admit Furthermore, the proves organized rays, where origin ray does...

Let k be an integral domain, n a positive integer, X a generic n×n matrix over k (i.e., the matrix (xij) over a polynomial ring k[xij ] in n 2 indeterminates xij), and adj(X) its classical adjoint. For char k = 0 it is shown that if n is odd, adj(X) is not the product of two noninvertible n×n matrices over k[xij ], while for n even, only one particular sort of factorization can occur. Whether t...

The increase of heavy metals concentration in soils is potentially threatening the environment and human health. In this paper, multivariate analysis methods such as Positive Matrix Factorization (PMF), Principal Component Analysis (PCA) and Cluster Analysis (CA) combined with geostatistical method were employed to identify the potential sources of soil pollution. A collection of 103 samples we...

In this paper we address the problem of matrix factorization on compressively-sampled measurements which are obtained by random projections. While this approach improves the scalability of matrix factorization, its performance is not satisfactory. We present a matrix co-factorization method where compressed measurements and a small number of uncompressed measurements are jointly decomposed, sha...