We present the semilocal convergence of a multi-step modified Newton-Hermitian and Skew-Hermitian Splitting method (MMN-HSS method) to approximate a solution of a nonlinear equation. Earlier studies show convergence under only Lipschitz conditions limiting the applicability of this method. The convergence in this study is shown under generalized Lipschitz-type conditions and restricted converge...

We study the CSCS method for large Hermitian positive definite Toeplitz linear systems, which first appears in Ng’s paper published in Ng, 2003 , and CSCS stands for circulant and skew circulant splitting of the coefficient matrix A. In this paper, we present a new iteration method for the numerical solution of Hermitian positive definite Toeplitz systems of linear equations. The method is a tw...

We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of (J2 = ±1)-metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among con...

The classical Airy function has been generalised by Kontsevich to a function of a matrix argument, which is an integral over the space of (skew) hermitian matrices of a unitary-invariant exponential kernel. In this paper, the Kontsevich integral is generalised to integrals over the Lie algebra of an arbitrary connected compact Lie group, using exponential kernels invariant under the group. The ...

For the unitary ensembles of N × N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2 × 2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an an...

A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH(G), is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH(G), which combines the cases of undirected and oriented unicyclic ...

We present a fast condition estimation algorithm for the eigenvalues of a class of structured matrices. These matrices are low rank modifications to Hermitian, skew-Hermitian, and unitary matrices. Fast structured operations for these matrices are presented, including Schur decomposition, eigenvalue block swapping, matrix equation solving, compact structure reconstruction, etc. Compact semisepa...

We consider preconditioned iterative methods applied to discretizations of the linearized Navier–Stokes equations in twoand three-dimensional bounded domains. Both unsteady and steady flows are considered. The equations are linearized by Picard iteration. We make use of the rotation form of the momentum equations, which has several advantages from the linear algebra point of view. We focus on a...

in this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. also, we represent several theorems for constructing each generalized skew t-normal distribution. next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, nickel and vanadium, associated with crude oil in shadgan wetland in the south-...

The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only i...