scholarly journals Block Preconditioned SSOR Methods for -Matrices Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Zhao-Nian Pu ◽  
Xue-Zhong Wang
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Iterative Methods ◽  
Spectral Radius ◽  
Numerical Examples ◽  
Comparison Results ◽  
Block Preconditioner

We present a block preconditioner and consider block preconditioned SSOR iterative methods for solving linear system . When is an -matrix, the convergence and some comparison results of the spectral radius for our methods are given. Numerical examples are also given to illustrate that our methods are valid.

Comparison Results between Jacobi and USSOR Iterative Methods

2014 ◽  
Vol 989-994 ◽  
pp. 1790-1793
Author(s):  
Ting Zhou ◽  
Shi Guang Zhang
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Spectral Radius ◽  
Numerical Example ◽  
Iteration Matrix ◽  
Comparison Results ◽  
Jacobi Iteration

In this paper, some comparison results between Jacobi and USSOR iteration for solving nonsingular linear systems are presented. It is showed that spectral radius of Jacobi iteration matrix B is less than that of USSOR iterative matrix under some conditions. A numerical example is also given to illustrate our results.

scholarly journals New iterative methods for dense linear systems

2021 ◽  
Vol 293 ◽  
pp. 02013
Author(s):  
Jinmei Wang ◽  
Lizi Yin ◽  
Ke Wang
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Iterative Methods ◽  
Parallel Implementation ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Linear System Of Equations ◽  
Dense Linear System ◽  
Linear Systems Of Equations

Solving dense linear systems of equations is quite time consuming and requires an efficient parallel implementation on powerful supercomputers. Du, Zheng and Wang presented some new iterative methods for linear systems [Journal of Applied Analysis and Computation, 2011, 1(3): 351-360]. This paper shows that their methods are suitable for solving dense linear system of equations, compared with the classical Jacobi and Gauss-Seidel iterative methods.

Certain efficient iterative methods for bipolar fuzzy system of linear equations

2020 ◽  
Vol 39 (3) ◽  
pp. 3971-3985 ◽  
Author(s):  
Muhammad Saqib ◽  
Muhammad Akram ◽  
Shahida Bashir
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Iterative Methods ◽  
Fuzzy Set ◽  
Fuzzy System ◽  
Linear Equations ◽  
Performance Validity ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Iterative Schemes

A bipolar fuzzy set model is an extension of fuzzy set model. We develop new iterative methods: generalized Jacobi, generalized Gauss-Seidel, refined Jacobi, refined Gauss-seidel, refined generalized Jacobi and refined generalized Gauss-seidel methods, for solving bipolar fuzzy system of linear equations(BFSLEs). We decompose n ×  n BFSLEs into 4n ×  4n symmetric crisp linear system. We present some results that give the convergence of proposed iterative methods. We solve some BFSLEs to check the validity, efficiency and stability of our proposed iterative schemes. Further, we compute Hausdorff distance between the exact solutions and approximate solution of our proposed schemes. The numerical examples show that some proposed methods converge for the BFSLEs, but Jacobi and Gauss-seidel iterative methods diverge for BFSLEs. Finally, comparison tables show the performance, validity and efficiency of our proposed iterative methods for BFSLEs.

A two-step iterative method based on diagonal and off-diagonal splitting for solving linear systems

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1441-1452
Author(s):  
Mehdi Dehghana ◽  
Marzieh Dehghani-Madisehb ◽  
Masoud Hajarianc
Keyword(s):  
Numerical Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Classical Problem ◽  
Coefficient Matrix ◽  
New Method ◽  
Step Method ◽  
Numerical Examples ◽  
Special Cases ◽  
Two Parameter

Solving linear systems is a classical problem of engineering and numerical analysis which has various applications in many sciences and engineering. In this paper, we study efficient iterative methods, based on the diagonal and off-diagonal splitting of the coefficient matrix A for solving linear system Ax = b, where A ? Cnxn is nonsingular and x,b ? Cnxm. The new method is a two-parameter two-step method that has some iterative methods as its special cases. Numerical examples are presented to illustrate the effectiveness of the new method.

scholarly journals Perfect observer resistant to the changes of dynamics of the standard linear system

2017 ◽  
Vol 65 (3) ◽  
pp. 313-316
Author(s):  
M. A. Sławiński
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Numerical Examples ◽  
Standard Linear ◽  
Time Linear

AbstractThe article presents a class of perfect observers for standard continuous-time linear systems. Observers are resistant to significant changes in the dynamics of the system. The value of poles of the system can be unlimited as long as their number does not change and the conditions presented in this article are satisfied. There are presented numerical examples and simulations results.

scholarly journals Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 62 (4) ◽  
pp. 889-895 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Reduced Order ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor reduced-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is given and is demonstrated on two numerical examples.

scholarly journals A convergence analysis of SOR iterative methods for linear systems with weak H-matrices

2016 ◽  
Vol 14 (1) ◽  
pp. 747-760
Author(s):  
Cheng-yi Zhang ◽  
Zichen Xue ◽  
Shuanghua Luo
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Convergence Results ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant ◽  
Necessary And Sufficient

AbstractIt is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.

scholarly journals Fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 24 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.

scholarly journals Stability Analysis of 2D Discrete Linear System Described by the Fornasini-Marchesini Second Model with Actuator Saturation

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Richa Negi ◽  
Haranath Kar ◽  
Shubhi Purwar
Keyword(s):  
Stability Analysis ◽  
Linear System ◽  
State Space ◽  
Linear Systems ◽  
Actuator Saturation ◽  
Discrete Systems ◽  
Stability Conditions ◽  
Numerical Examples ◽  
Discrete Linear Systems ◽  
2D Discrete Systems

This paper proposes a novel antiwindup controller for 2D discrete linear systems with saturating controls in Fornasini-Marchesini second local state space (FMSLSS) setting. A Lyapunov-based method to design an antiwindup gain of 2D discrete systems with saturating controls is established. Stability conditions allowing the design of antiwindup loops, in both local and global contexts have been derived. Numerical examples are provided to illustrate the applicability of the proposed method.

Convergence Analysis of Preconditioned SSOR Iterative Method for Linear Systems

2014 ◽  
Vol 644-650 ◽  
pp. 1988-1991
Author(s):  
Ting Zhou
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Convergence Result ◽  
Numerical Example ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

For solving the linear system, different preconditioned iterative methods have been proposed by many authors. In this paper, we present preconditioned SSOR iterative method for solving the linear systems. Meanwhile, we apply the preconditioner to H-matrix and obtain the convergence result. Finally, a numerical example is also given to illustrate our results.

Sign in / Sign up

Export Citation Format

Share Document