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.

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.

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

2017 ◽  
Vol 7 (4) ◽  
pp. 827-836
Author(s):  
Ze-Jia Xie ◽  
Xiao-Qing Jin ◽  
Zhi Zhao
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
Indefinite Systems ◽  
Indefinite Linear Systems ◽  
Theoretical Results

AbstractSome convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

scholarly journals H-Matrices in Fuzzy Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Saberi Najafi ◽  
S. A. Edalatpanah
Keyword(s):  
Linear System ◽  
Theoretical Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

We consider a class of fuzzy linear system of equations and demonstrate some of the existing challenges. Furthermore, we explain the efficiency of this model when the coefficient matrix is an H-matrix. Numerical experiments are illustrated to show the applicability of the theoretical analysis.

scholarly journals Error Analysis of Randomized Runge–Kutta Methods for Differential Equations with Time-Irregular Coefficients

2017 ◽  
Vol 17 (3) ◽  
pp. 479-498 ◽  
Author(s):  
Raphael Kruse ◽  
Yue Wu
Keyword(s):  
Differential Equations ◽  
Error Analysis ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Quadrature Rule ◽  
Time Variable ◽  
Important Ingredient ◽  
Riemann Sum ◽  
Runge Kutta ◽  
Theoretical Results

AbstractThis paper contains an error analysis of two randomized explicit Runge–Kutta schemes for ordinary differential equations (ODEs) with time-irregular coefficient functions. In particular, the methods are applicable to ODEs of Carathéodory type, whose coefficient functions are only integrable with respect to the time variable but are not assumed to be continuous. A further field of application are ODEs with coefficient functions that contain weak singularities with respect to the time variable. The main result consists of precise bounds for the discretization error with respect to the {L^{p}(\Omega;{\mathbb{R}}^{d})}-norm. In addition, convergence rates are also derived in the almost sure sense. An important ingredient in the analysis are corresponding error bounds for the randomized Riemann sum quadrature rule. The theoretical results are illustrated through a few numerical experiments.

A NONCONFORMING PENALTY METHOD FOR A TWO-DIMENSIONAL CURL–CURL PROBLEM

2009 ◽  
Vol 19 (04) ◽  
pp. 651-668 ◽  
Author(s):  
SUSANNE C. BRENNER ◽  
FENGYAN LI ◽  
LI-YENG SUNG
Keyword(s):  
Numerical Experiments ◽  
Vector Fields ◽  
Convergence Rates ◽  
Two Dimensional ◽  
Weakly Continuous ◽  
Graded Meshes ◽  
Optimal Convergence Rates ◽  
Maxwell Eigenvalues ◽  
Theoretical Results ◽  
Convergence Of The Scheme

A nonconforming finite element method for a two-dimensional curl–curl problem is studied in this paper. It uses weakly continuous P1 vector fields and penalizes the local divergence. Two consistency terms involving the jumps of the vector fields across element boundaries are also included to ensure the convergence of the scheme. Optimal convergence rates (up to an arbitrary positive ∊) in both the energy norm and the L2 norm are established on graded meshes. This scheme can also be used in the computation of Maxwell eigenvalues without generating spurious eigenmodes. The theoretical results are confirmed by numerical experiments.

scholarly journals An Iterative Method for Symmetric Positive Semidefinite Linear System of Equations

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
Davod Khojasteh Salkuyeh
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Numerical Experiments ◽  
Positive Semidefinite ◽  
Sufficient Condition ◽  
System Of Equations ◽  
Linear System Of Equations

AbstractIn this paper, a new two-step iterative method for solving symmetric positive semidefinite linear system of equations is presented. A sufficient condition for the semiconvergence of the method is also given. Some numerical experiments are presented to show the efficiency of the proposed method.

Convergence Results of the Improving Modified Gauss-Seidel (IMGS) Iterative Method for a Symmetric Positive Definite Matrix

2014 ◽  
Vol 989-994 ◽  
pp. 1794-1797
Author(s):  
Shi Guang Zhang ◽  
Ting Zhou
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Convergence Rates ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Symmetric Positive Definite Matrix ◽  
Symmetric Positive Definite ◽  
Convergence Results ◽  
Comparison Results

In this paper, in order to improve the convergence rates of iterative method solving the linear system, the improving modified Gauss-Seidel (IMGS) iterative method with a preconditioner is proposed. Some convergence and comparison results are given when is a symmetric definite matrix are provided.

New Convergence of Relaxed Parallel Multisplitting Method for the H-Matrix

2013 ◽  
Vol 756-759 ◽  
pp. 3162-3166
Author(s):  
You Lin Zhang ◽  
Li Tao Zhang
Keyword(s):  
Linear System ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Iterative Method ◽  
Coefficient Matrix ◽  
Convergence Domain ◽  
Multisplitting Method ◽  
Multisplitting Methods ◽  
Relaxed Multisplitting Method

Relaxed technique is one of the main techniques for Improving convergence rate of splitting iterative method. Based on existing parallel multisplitting methods, we have deeply studied the convergence of the relaxed multisplitting method associated with TOR multisplitting for solving the linear system whose coefficient matrix is an H-matrix. Moreover, theoretical analysis have shown that the convergence domain of the relaxed parameters is weaker and wider.

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