Vectorized Parallel Solver for Tridiagonal Toeplitz Systems of Linear Equations

2020 ◽  
pp. 93-103
Author(s):  
Beata Dmitruk ◽  
Przemysław Stpiczyński
Keyword(s):  
Linear Equations ◽  
Parallel Solver ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems

A Superfast Algorithm for Toeplitz Systems of Linear Equations

2008 ◽  
Vol 29 (4) ◽  
pp. 1247-1266 ◽  
Author(s):  
S. Chandrasekaran ◽  
M. Gu ◽  
X. Sun ◽  
J. Xia ◽  
J. Zhu
Keyword(s):  
Linear Equations ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems ◽  
Superfast Algorithm

An Improved Fast Algorithm for Solving Toeplitz Systems in Mechanical Control

2011 ◽  
Vol 55-57 ◽  
pp. 863-867
Author(s):  
Li Chao Tian ◽  
Hong Kui Li
Keyword(s):  
Fast Algorithm ◽  
Toeplitz Matrices ◽  
Linear Equations ◽  
Mechanical Control ◽  
Systems Of Linear Equations ◽  
Toeplitz Systems

Pentadiagonal Toeplitz systems of linear equations arise in many application areas. Because of the structure and many good properties of pentadiagonal Toeplitz matrices, they have been applied in Mechanical Control. Based on [1], in this paper, we present an improved fast algorithm for solving symmetric pentadiagonal 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.

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