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1. CMB 2017 (vol 60 pp. 807)

Liu, Zhongyun; Qin, Xiaorong; Wu, Nianci; Zhang, Yulin
 The Shifted Classical Circulant and Skew Circulant Splitting Iterative Methods for Toeplitz Matrices It is known that every Toeplitz matrix $T$ enjoys a circulant and skew circulant splitting (denoted by CSCS) i.e., $T=C-S$ with $C$ a circulant matrix and $S$ a skew circulant matrix. Based on the variant of such a splitting (also referred to as CSCS), we first develop classical CSCS iterative methods and then introduce shifted CSCS iterative methods for solving hermitian positive definite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical CSCS iterative methods work slightly better than the Gauss-Seidel (GS) iterative methods if the CSCS is convergent, and that there is always a constant $\alpha$ such that the shifted CSCS iteration converges much faster than the Gauss-Seidel iteration, no matter whether the CSCS itself is convergent or not. Keywords:Hermitian positive definite, CSCS splitting, Gauss-Seidel splitting, iterative method, Toeplitz matrixCategories:15A23, 65F10, 65F15

2. CMB 2016 (vol 60 pp. 269)

Chen, Jianlong; Zhu, Huihui; Patricio, Pedro; Zhang, Yulin
 Characterizations and Representations of Core and Dual Core Inverses In this paper, double commutativity and the reverse order law for the core inverse are considered. Then, new characterizations of the Moore-Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered. Keywords:regularities, group inverses, Moore-Penrose inverses, core inverses, dual core inverses, Dedekind-finite ringsCategories:15A09, 15A23

3. CMB 1998 (vol 41 pp. 178)

Krupnik, Ilya; Lancaster, Peter
 Minimal pencil realizations of rational matrix functions with symmetries A theory of minimal realizations of rational matrix functions $W(\lambda)$ in the pencil'' form $W(\lambda)=C(\lambda A_1-A_2)^{-1}B$ is developed. In particular, properties of the pencil $\lambda A_1-A_2$ are discussed when $W(\lambda)$ is hermitian on the real line, and when $W(\lambda)$ is hermitian on the unit circle. Categories:93Bxx, 15A23
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