Circulant and skew-circulant preconditioners for skew-hermitian type Toeplitz systems

1991 ◽  
Vol 31 (4) ◽  
pp. 632-646 ◽  
Author(s):  
Raymond H. Chan ◽  
Xiao-Qing Jin
Keyword(s):  
Skew Circulant ◽  
Circulant Preconditioners ◽  
Toeplitz Systems

The Best Circulant Preconditioners for Hermitian Toeplitz Systems

2000 ◽  
Vol 38 (3) ◽  
pp. 876-896 ◽  
Author(s):  
Raymond H. Chan ◽  
Andy M. Yip ◽  
Michael K. Ng
Keyword(s):  
Circulant Preconditioners ◽  
Toeplitz Systems

The best circulant preconditioners for Hermitian Toeplitz systems II: The multiple-zero case

2002 ◽  
Vol 92 (1) ◽  
pp. 17-40 ◽  
Author(s):  
Raymond H. Chan ◽  
Michael K. Ng ◽  
Andy M. Yip
Keyword(s):  
Multiple Zero ◽  
Circulant Preconditioners ◽  
Toeplitz Systems

scholarly journals Accelerated Circulant and Skew Circulant Splitting Methods for Hermitian Positive Definite Toeplitz Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
N. Akhondi ◽  
F. Toutounian
Keyword(s):  
Convergence Property ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Optimal Parameters ◽  
Skew Circulant ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems ◽  
Two Parameters ◽  
Two Parameter

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 . 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 two-parameter generation of the CSCS method such that when the two parameters involved are equal, it coincides with the CSCS method. We discuss the convergence property and optimal parameters of this method. Finally, we extend our method to BTTB matrices. Numerical experiments are presented to show the effectiveness of our new method.

scholarly journals The Shifted Classical Circulant and Skew Circulant Splitting Iterative Methods for Toeplitz Matrices

2017 ◽  
Vol 60 (4) ◽  
pp. 807-815 ◽  
Author(s):  
Zhongyun Liu ◽  
Xiaorong Qin ◽  
Nianci Wu ◽  
Yulin Zhang
Keyword(s):  
Iterative Methods ◽  
Toeplitz Matrix ◽  
Numerical Experiments ◽  
Toeplitz Matrices ◽  
Skew Circulant ◽  
Toeplitz Systems ◽  
Better Than

AbstractIt is known that every Toeplitz matrix T enjoys a circulant and skew circulant splitting (denoted CSCS) i.e., T = C−S with C a circulantmatrix and S a skew circulantmatrix. 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 deûnite 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 α such that the shifted CSCS iteration converges much faster than the Gauss–Seidel iteration, no matter whether the CSCS itself is convergent or not.

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