In this paper we study a nonlinear elliptic system of equations imposed on a map from a complete Hermitian (non-Kähler) manifold to a Riemannian manifold. This system is more appropriate to Hermitian geometry than the harmonic map system since it is compatible with the holomorphic structure of the domain manifold in the sense that holomorphic maps are Hermitian harmonic maps. It was first studi...

A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The theoretical spectral analysis focuses on the case of matrix sequences related to FE approximations on uniform structured meshes, by referring to spectral tools der...

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...

Non-Hermitian but PφTφ-symmetrized spherically-separable Dirac and Schrödinger Hamiltonians are considered. It is observed that the descendant Hamiltonians Hr, Hθ, and Hφ play essential roles and offer some ”user-feriendly” options as to which one (or ones) of them is (or are) nonHermitian. Considering a PφTφ-symmetrized Hφ, we have shown that the conventional Dirac (relativistic) and Schröding...

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...

Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing xn − λ over Fq2 is given, where λ is a unit in Fq2 . Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over Fq2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dua...

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyperpseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and ⋆-scalar curvature.

The need to compute expressions of the form uf(A)v, where A is a large square matrix, u and v are vectors, and f is a function, arises in many applications, including network analysis, quantum chromodynamics, and the solution of linear discrete ill-posed problems. Commonly used approaches first reduce A to a small matrix by a few steps of the Hermitian or non-Hermitian Lanczos processes and the...

We perform a backward error analysis of the inexact shift-and-invert Arnoldi algorithm. We consider inexactness in the solution of the arising linear systems, as well as in the orthonormalization steps, and take the non-orthonormality of the computed Krylov basis into account. We show that the computed basis and Hessenberg matrix satisfy an exact shift-and-invert Krylov relation for a perturbed...