Non-symmetric and symmetric twisted block factorizations of block tridiagonal matrices are discussed. In contrast to non-blocked factorizations of this type, localized pivoting strategies can be integrated which improves numerical stability without causing any extra fill-in. Moreover, the application of such factorizations for approximating an eigenvector of a block tridiagonal matrix, given an...

We study connections between operator theoretic properties of Toeplitz operators acting on suitable Besikovitch spaces and factorizations of their symbols which are matrix valued almost periodic functions of several real variables. Among other things, we establish the existence of a twisted canonical factorization for locally sectorial symbols, and characterize one-sided invertibility of Toepli...

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

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 prove that the Hurwitz equivalence problem for 1-factorizations in F2⊕F2 is undecidable, and as a consequence, the Hurwitz equivalence problem for ∆-factorizations in the braid groups Bn, n ≥ 5 is also undecidable.

The success of matrix factorizations such as the singular value decomposition (SVD) has motivated search for even more factorizations. We catalog 53 factorizations, most which we believe to be new. Our systematic approach, inspired by generalized Cartan Lie theory, also encompasses known SVD, symmetric eigendecomposition, CS decomposition, hyperbolic structured SVDs, Takagi factorization, and o...

It has been recently observed that fundamental aspects of the classical theory factorization can be greatly generalized by combining languages monoids and preorders. This led to various theorems on existence certain factorizations, herein called ⪯-factorizations, for ⪯-non-units a (multiplicatively written) monoid H endowed with preorder ⪯, where an element u∈H is ⪯-unit if u⪯1H⪯u ⪯-non-unit ot...

We study the number of ways of writing a positive integer n as a product of integer factors greater than one. We survey methods from the literature for enumerating and also generating lists of such factorizations for a given number n. In addition, we consider the same questions with respect to factorizations that satisfy constraints, such as having all factors distinct. We implement all these m...

The one-factorizations of the complete 3-uniform hypergraph with 9 vertices, K 9 , are classified by means of an exhaustive computer search. It is shown that the number of isomorphism classes of such one-factorizations is 103 000.