Abstract This chapter considers the LU factorization of a general nonsymmetric nonsingular sparse matrix A . In practice, numerical pivoting for stability and/or ordering to limit fill-in in factors is often needed and computed then permuted PAQ Pivoting discussed Chapter 7 algorithms 8

Nonnegative matrix factorizations are often encountered in data mining applications where they used to explain datasets by a small number of parts. For many these it is desirable that there exists unique nonnegative factorization up trivial modifications given scalings and permutations. This means model parameters uniquely identifiable from the data. Rigidity theory bar joint frameworks field s...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface, and also define a functor to the stable module category of maximal Cohen-Macaulay modules on the hypersurface. We introduce a new functorial concept of matrix factorizations for complete intersections that allows us to describe the asymptotic structure of mi...

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

In this paper, we count factorizations of Coxeter elements in wellgenerated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factorizations, which is expressed uniformly in terms of natural parameters of the group. In the case of factorizations of minimal length, we recover a formula due to P. Deligne, J. ...

Some general remarks are made about likelihood factorizations, distinguishing parameter-based factorizations and concentration-graph factorizations. Two parametric families of distributions for mixed discrete and continuous variables are discussed. Conditions on graphs are given for the circumstances under which their joint analysis can be split into separate analyses, each involving a reduced ...

The paper presents a novel Newton method for constructing canonical Wiener-Hopf factorizations of complex matrix polynomials and spectral factorizations of positive definite matrix polynomials. The factorizations are the ones needed for discrete-time linear systems and hence with respect to the unit circle. The Jacobi matrix is analyzed, and the convergence of the method is proved and tested nu...