Finite integration methods for isospectral flows

In this paper we consider the approximate computation of isospectral flows based on finite integration methods( FIM) with radial basis functions( RBF) interpolation,a new algorithm is developed. Our method ensures the symmetry of the solutions. Numerical experiments demonstrate that the solutions have higher accuracy by our algorithm than by the second order Runge- Kutta( RK2) method

On the eigenstructure of hermitian Toeplitz matrices with prescribed eigenpairs

In this paper we concern the spectral properties of hermitian Toeplitz matrices. 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 Toeplitz matrices and then discuss a related inverse eigenproblem. We show that the dimension of the subspace of hermitian Toeplitz matrices with two given eigenvectors is at least two and independent of the size of the matrix, the solution of the inverse hermitian Toeplitz eigenproblem with two given eigenpairs is unique.FC

The reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs

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 re- duced to a real matrix by a simple similarity transformation, we rst consider the eigenstructure of hermitian Toeplitz matrices and then discuss a related reconstruction problem. We show that the di- mension of the subspace of hermitian Toeplitz matrices with two given eigenvectors is at least two and independent of the size of the matrix, and the solution of the reconstruction problem of an hermitian Toeplitz matrix with two given eigenpairs is unique.Fundação para a Ciência e a Tecnologia (FCT) - Research Programme POCTINational Natural Science Foundation of China - nº 10771022, 10571012Scienti c Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry of China - nº 890 (2008)Major Foundation of Educational Committee of Hunan Province - nº 09A002 (2009

Computing the square roots of matrices with central symmetry

For computing square roots of a nonsingular matrix A, which are functions of A, two well known fast and stable algorithms, which are based on the Schur decomposition of A, were proposed by Bj¨ork and Hammarling [3], for square roots of general complex matrices, and by Higham [10], for real square roots of real matrices. In this paper we further consider (the computation of) the square roots of matrices with central symmetry. We first investigate the structure of the square roots of these matrices and then develop several algorithms for computing the square roots. We show that our algorithms ensure significant savings in computational costs as compared to the use of standard algorithms for arbitrary matrices.Fundação para a Ciência e a Tecnologia (FCT

m-step preconditioners for nonhermitian positive definite Toeplitz systems

It is known that if A is a Toeplitz matrix，then A enjoys a circulant and skew circulant splitting(de— noted by CSCS)，i．e．，A=C+ S with C a circulant matrix and S a skew circulant matrix． Based on the CSCS iteration，we give m-step preconditioners P for certain classes of Toeplitz matrices in this paper．We show that if both C and S are positive definite，then the spectrum of the preconditioned matrix(PA)^* PA are clustered around one for some moderate size ． Experimental results show that the proposed preconditioners perform slightly better than T．Chan’S preconditioners for some moderate size m．info:eu-repo/semantics/publishedVersio

Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices

The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamiltonian square roots. Compared to the standard real Schur method, which ignores the structure, this method requires significantly less arithmetic.National Natural Science Foundations of China, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry,Fundação para a Ciência e a Tecnologia (FCT

On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks

We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric matrices. Then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum. We have implemented our ideas in a Matlab code. Numerical results produced with this code are included.Fundação para a Ciência e a Tecnologia (FCT

Stationary splitting iterative methods for the matrix equation AX B = C

Stationary splitting iterative methods for solving AXB = Care considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A = M −N by a matrix H such that (I −H) invertible. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface fitting applications, our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer-aided geometric design (CAGD).The authors would like to thank the supports of the National Natural Science Foundation of China under Grant No. 11371075, the Hunan Key Laboratory of mathematical modeling and analysis in engineering, and the Portuguese Funds through FCT–Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013

Structure-preserving Schur methods for computing square roots of real skew-Hamiltonian matrices

Our contribution is two-folded. First, starting from the known fact that every real skew-Hamiltonian matrix has a real Hamiltonian square root, we give a complete characterization of the square roots of a real skew-Hamiltonian matrix W. Second, we propose a structure exploiting method for computing square roots of W. Compared to the standard real Schur method, which ignores the structure, our method requires significantly less arithmetic.Comment: 27 pages; Conference "Directions in Matrix Theory 2011", July 2011, University of Coimbra, Portuga