scholarly journals The Four-Parameter PSS Method for Solving the Sylvester Equation

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 105 ◽  
Author(s):  
Hai-Long Shen ◽  
Yan-Ran Li ◽  
Xin-Hui Shao
Keyword(s):  
Iterative Method ◽  
Numerical Experiment ◽  
Coefficient Matrix ◽  
Sylvester Equation ◽  
Iteration Number

In order to solve the Sylvester equations more efficiently, a new four parameters positive and skew-Hermitian splitting (FPPSS) iterative method is proposed in this paper based on the previous research of the positive and skew-Hermitian splitting (PSS) iterative method. We prove that when coefficient matrix A and B satisfy certain conditions, the FPPSS iterative method is convergent in the parameter’s value region. The numerical experiment results show that compared with previous iterative method, the FPPSS iterative method is more effective in terms of iteration number IT and runtime.

scholarly journals An Iterative Method Using Piecewise Valued Basic Vectors for Solving Linear Systems with Symmetric Coefficient Matrix

2004 ◽  
Vol 7 ◽  
pp. 247-254
Author(s):  
Takuro KATAYAMA ◽  
Mitsuhiro KASHIWAGI ◽  
Shin-ichi OHWAKI ◽  
Toshitaka YAMAO
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Coefficient Matrix

A symmetric preserving iterative method for generalized Sylvester equation

2010 ◽  
Vol 13 (3) ◽  
pp. 408-417 ◽  
Author(s):  
Jiao-Fen Li ◽  
Xi-Yan Hu ◽  
Xue-Feng Duan
Keyword(s):  
Iterative Method ◽  
Sylvester Equation ◽  
Generalized Sylvester Equation

Convergence of the Preconditioned AOR Method for an H-Matrix

2013 ◽  
Vol 756-759 ◽  
pp. 2615-2619
Author(s):  
Jie Jing Liu
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Triangular Matrix ◽  
Coefficient Matrix ◽  
Aor Method ◽  
Upper Triangular Matrix ◽  
Theoretical Results

Linear system with H-matrix often appears in a wide variety of areas and is studied by many numerical researchers. In order to improve the convergence rates of iterative method solving the linear system whose coefficient matrix is an H-matrix. In this paper, a preconditioned AOR iterative method with a multi-parameters preconditioner with a general upper triangular matrix is proposed. In addition, the convergence of the coressponding iterative method are established. Lastly, we provide numerical experiments to illustrate the theoretical results.

SEBSM-Based Iterative Method for Solving Large Systems of Linear Equations and Its Applications in Engineering Computation

2016 ◽  
Vol 13 (05) ◽  
pp. 1650024 ◽  
Author(s):  
Jin-Xiu Hu ◽  
Xiao-Wei Gao ◽  
Zhi-Chao Yuan ◽  
Jian Liu ◽  
Shi-Zhang Huang
Keyword(s):  
Iterative Method ◽  
Direct Method ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Relaxation Factor ◽  
Banded Matrix ◽  
Speed Up ◽  
Systems Of Linear Equations ◽  
Matrix Formula ◽  
Large Systems

In this paper, a new iterative method, for solving sparse nonsymmetrical systems of linear equations is proposed based on the Simultaneous Elimination and Back-Substitution Method (SEBSM), and the method is applied to solve systems resulted in engineering problems solved using Finite Element Method (FEM). First, SEBSM is introduced for solving general linear systems using the direct method. And, then an iterative method based on SEBSM is presented. In the method, the coefficient matrix [Formula: see text] is split into lower, diagonally banded and upper matrices. The iterative convergence can be controlled by selecting a suitable bandwidth of the diagonally banded matrix. And the size of the working array needing to be stored in iteration is as small as the bandwidth of the diagonally banded matrix. Finally, an accelerating strategy for this iterative method is proposed by introducing a relaxation factor, which can speed up the convergence effectively if an optimal relaxation factor is chosen. Two numerical examples are given to demonstrate the behavior of the proposed method.

scholarly journals On single-step HSS iterative method with circulant preconditioner for fractional diffusion equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mu-Zheng Zhu ◽  
Guo-Feng Zhang ◽  
Ya-E Qi
Keyword(s):  
Iterative Method ◽  
Coefficient Matrix ◽  
Fractional Diffusion ◽  
Single Step ◽  
Diffusion Equations ◽  
Preconditioned Conjugate Gradient ◽  
Fractional Diffusion Equations ◽  
Finite Difference Discretization ◽  
Circulant Preconditioners ◽  
Pcg Method

Abstract By exploiting Toeplitz-like structure and non-Hermitian dense property of the discrete coefficient matrix, a new double-layer iterative method called SHSS-PCG method is employed to solve the linear systems originating from the implicit finite difference discretization of fractional diffusion equations (FDEs). The method is a combination of the single-step Hermitian and skew-Hermitian splitting (SHSS) method with the preconditioned conjugate gradient (PCG) method. Further, the new circulant preconditioners are proposed to improve the efficiency of SHSS-PCG method, and the computation cost is further reduced via using the fast Fourier transform (FFT). Theoretical analysis shows that the SHSS-PCG iterative method with circulant preconditioners is convergent. Numerical experiments are given to show that our SHSS-PCG method with circulant preconditioners preforms very well, and the proposed circulant preconditioners are very efficient in accelerating the convergence rate.

A Preconditioned AOR Iterative Method for an H-Matrix

2014 ◽  
Vol 644-650 ◽  
pp. 1984-1987
Author(s):  
Shi Guang Zhang
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Triangular Matrix ◽  
Coefficient Matrix ◽  
Numerical Example ◽  
Upper Triangular Matrix

The paper presents a preconditioned AOR iterative method if preconditioner is a general upper triangular matrix for solving a linear system whose coefficient matrix is an H-matrix. In addition, we discuss the convergence of corresponding methods. Finally, a numerical example is also given to illustrate our results.

Sign in / Sign up

Export Citation Format

Share Document