We present our work on the sparse Cholesky factorization using a hypermatrix data structure. First, we provide some background on the sparse Cholesky factorization and explain the hypermatrix data structure. Next, we present the matrix test suite used. Afterwards, we present the techniques we have developed in pursuit of performance improvements for the sparse hypermatrix Cholesky factorization...

In this article the notions of quasi mono (epi) as a generalization (epi), (quasi weakly hereditary) general closure operator $mathbf{C}$ on category $mathcal{X}$ with respect to class $mathcal{M}$ morphisms, and factorization structures in are introduced. It is shown that under certain conditions, if $(mathcal{E}, mathcal{M})$ structure $mathcal{X}$, then has right $mathcal{M}$-factorization l...

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

BK-factorization of bivariate LPDOs is outlined. As an example, class of factorized hyperbolic operators is constructed as well as general solution in quadratures for operators of this class. Coupling of BK-factorization with Darboux-Laplace transformations is described which provided additional factorization conditions (demand of generalized commutativity) in the case when BK-factorization doe...

Recently, recovery of non-rigid structure by the factorization algorithms have received attention in the literature. The factorization algorithm decomposes the feature points over the given image sequence into motion of the camera and 3D shape bases. The non-rigid structure can be represented by the linear combination of the 3D shape bases. Although the closed-form solution of the non-rigid fac...

We compare results on diffractive W-boson production at the Tevatron with predictions based on the diffractive structure function measured in deep inelastic scattering at HERA assuming (a) conventional factorization or (b) hard factorization combined with a rapidity gap distribution scaled to the total gap probability. We find that conventional factorization fails, while the scaling prediction ...

An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing factorization problem is nonconvex. An alternating projections algorithm is developed, which is ...