Let V be 2n-dimensional vector space over a field K equipped with a nondegenerate skew-ψ-Hermitian form f of Witt index n ≥ 1, let K0 ⊆ K be the fix field of ψ and let G denote the group of isometries of (V, f). For every k ∈ {1, . . . , 2n}, there exist natural representations of the groups G ∼= U(2n,K/K0) and H = G∩SL(V ) ∼= SU(2n,K/K0) on the k-th exterior power of V . With the aid of linear...

We study the curvature of almost Hermitian manifolds and their special analogues via intrinsic torsion and representation theory. By deriving different forumlæ for the skew-symmetric part of the ∗-Ricci curvature, we find that some of these contributions are dependent on the approach used, and for the almost Hermitian case we obtain tables that differ from those of Falcitelli, Farinola & Salamo...

We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspacemethods.We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditi...

*Correspondence: [email protected] School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, P.R. China Abstract In this paper, based on the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method, the nonlinear MHSS-like iteration method is presented to solve a class of the weakly absolute value equations (AVE). By using a smoothing approximate function, the...

We present results connecting the shape of the numerical range to intrinsic properties of a matrix A. When A is a nonnegative matrix, these results are to a large extent analogous to the Perron-Frobenius theory, especially as it pertains to irreducibility and cyclicity in the combinatorial sense. Special attention is given to polygonal, circular and elliptic numerical ranges. The main vehicles ...

We investigate the behavior of eigenvalues under structured perturbations. We show that for many common structures such as (complex) symmetric, Toeplitz, symmetric Toeplitz, circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations, and prove similar results for real perturbations. An exception are complex skewsymmetric matrice...

We investigate the performance of smoothers based on the Hermitian/skew-Hermitian (HSS) and augmented Lagrangian (AL) splittings applied to the Marker-and-Cell (MAC) discretization of the Oseen problem. Both steady and unsteady flows are considered. Local Fourier analysis and numerical experiments on a two-dimensional lid-driven cavity problem indicate that the proposed smoothers result in h-in...

In this note, we study the notion of structured pseudospectra. We prove that for Toeplitz, circulant and symmetric structures, the structured pseudospectrum equals the unstructured pseudospectrum. We show that this is false for Hermitian and skew-Hermitian structures. We generalize the result to pseudospectra of matrix polynomials. Indeed, we prove that the structured pseudospectrum equals the ...

We construct a preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration scheme for solving and preconditioning a class of block two-by-two linear systems arising from the Galerkin finite element discretizations of a class of distributed control problems. The convergence theory of this class of PMHSS iteration methods is established and the spectral properties of the PMHS...