Familiarly, in Z, we have unique factorization. We investigate the general ring and what conditions we can impose on it to necessitate analogs of unique factorization. The trivial ideal structure of a field, the extent to which primary decomposition is unique, that a Noetherian ring necessarily has one, that a principal ideal domain is a unique factorization domain, and that a Dedekind domain h...

This article aimed at a general audience of computational scientists, surveys the Cholesky factorization for symmetric positive definite matrices, covering algorithms for computing it, the numerical stability of the algorithms, and updating and downdating of the factorization. Cholesky factorization with pivoting for semidefinite matrices is also treated.  2009 John Wiley & Sons, Inc. WIREs Co...

This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first prove the factorization property. Then we provide moments formula. Lastly we present some applications of the factorization principle.

speciated samples of pm2.5 were collected at the hamshire and orange sites in golden triangle of texas by us epa (environmental protection agency) from july of 2003 to august of 2005. a total of 269 samples for the hamshire site and 293 samples for the orange site with 52 species were measured; however, 22 species were excluded because of too many below-detectionlimit data. among the 22 species...

A block representation of the BLU factorization for block tridiagonal matrices is presented. Some properties on the factors obtained in the course of the factorization are studied. Simpler expressions for errors incurred at the process of the factorization for block tridiagonal matrices are considered.

Spectral factorization methods are used for the estimation of minimum phase time series from a given power spectrum. We present an efficient technique for spectral factorization, based on Newton’s method. We show how to apply the method to the factorization of both auto and cross-spectra, and present a simple example of 2-D deconvolution in the helical coordinate system.

In this article, we present a study of the correlation between factorization and the quality criterion of traceability. Our work is based on a set of new factorization metrics and a specific definition of traceability. The results of our experiment show a good correlation between the increase of the factorization of a UML class diagram and its traceability.

This is a concise survey of some results and open problems concerning Wiener-Hopf factorization and almost periodic factorization of matrix functions. Several classes of discontinuous matrix functions are considered. Also sketched is the abstract framework which unifies the two types of factorization. Mathematics Subject Classification (2010). Primary 47A68; Secondary 30E25, 43A75, 45F15, 47B35 .