Toeplitz matrices have been found important applications in bioinformatics and computational biology [5-9, 11-12]. In this paper we concern the reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, we first consider the eigenstructure of hermitian Toe...

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify the available choices of methods and catalogue a...

In this paper we derive bounds on the eigenvalues of the preconditioned matrix that arises in the solution of saddle point problems when the Hermitian and skew-Hermitian splitting preconditioner is employed. We also give sufficient conditions for the eigenvalues to be real. A few numerical experiments are used to illustrate the quality of the bounds.

A generalized anti-hermitian staggered Dirac operator is formulated. Its relation with noncommutative geometry is briefly reviewed. Once this antihermitian operator is modified to be “γ5-hermitian”, it will provide a new solution to Ginsparg-Wilson relation, basing on an abstract algebraic analysis of Neuberger’s overlap construction and a redefinition of chirality.

In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

Two-stage iterative methods for the solution of linear systems are studied. Convergence of both stationary and nonstationary cases is analyzed when the coefficient matrix is Hermitian positive definite. Keywords—Linear systems, Hermitian matrices, Positive definite matrices, Iterative methods, Nonstationary methods, Two-stage methods.

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

In this paper, we present a naturally numerical method for finding the maximal hermitian solution X+ of the Discrete-Time Algebraic Riccati Equation (DTARE) based on the convergence of a monotone sequence of hermitian matrices. MIRAMARE TRIESTE August 1999 E-mail: [email protected] 227 Nguyen Van Cu, Q5, HCMC, Vietnam.

For a given linear matrix function A1−B1XB 1 , where X is a variable Hermitian matrix, this paper derives a group of closed-form formulas for calculating the global maximum and minimum ranks and inertias of the matrix function subject to a pair of consistent matrix equations B2XB ∗ 2 = A2 and B3XB ∗ 3 = A3. As applications, we give necessary and sufficient conditions for the triple matrix equat...