the triple factorization of a group $g$ has been studied recently showing that $g=aba$ for some proper subgroups $a$ and $b$ of $g$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. in this paper we study two infinite classes of non-abelian finite groups $d_{2n}$ and $psl(2,2^{n})$...

Abstract. This manuscript focuses on the development of a parallel QR-factorization of structured rank matrices, which can then be used for solving systems of equations. First, we will prove the existence of two types of Givens transformations, named rank decreasing and rank expanding Givens transformations. Combining these two types of Givens transformations leads to different patterns for ann...

By relating the projective camera model to the perspective one, the intrinsic camera parameters give rise to what is called the calibration matrix. This paper presents two new methods to retrieve the calibration matrix from the projective camera model. In both methods, a collective approach was adopted, using matrix representation. The calibration matrix was retrieved from a quadratic matrix te...

Contrary to what has been often claimed in the literature, we clarify that the hard photongluon cross section ∆σ hard(x) in polarized deep inelastic scattering calculated in the gauge-invariant factorization scheme does not involve any soft contributions and hence it is genuinely hard. We show that the polarized proton structure function g 1(x) up to the next-to-leading order of αs is independe...

Sturm-Triggs iteration is a standard method for solving the projective factorization problem. Like other iterative algorithms, this method suffers from some common drawbacks such as requiring a good initialization, the iteration may not converge or only converge to a local minimum, etc. None of the published works can offer any sort of global optimality guarantee to the problem. In this paper, ...

Funding Information Russian Science Foundation, Grant/Award Number: 14-31-00024 Summary The paper studies numerical properties of LU and incomplete LU factorizations applied to the discrete linearized incompressible Navier–Stokes problem also known as the Oseen problem. A commonly used stabilized Petrov–Galerkin finite element method for the Oseen problem leads to the system of algebraic equati...

This paper presents the design and implementation of a memory scalable parallel symbolic factorization algorithm for general sparse unsymmetric matrices. Our parallel algorithm uses a graph partitioning approach, applied to the graph of |A|+ |A| , to partition the matrix in such a way that is good for sparsity preservation as well as for parallel factorization. The partitioning yields a so-call...