Preconditioned AOR Iterative Method Research Articles

Performance of FSPAOR iteration for solving one-dimensional space-fractional diffusion equation

This paper considers the numerical solution of a one-dimensional space-fractional diffusion equation. To obtain the solution, we use an unconditionally stable implicit finite difference approximation with the Caputo’s space-fractional operator. We study on improving the convergence rate of the solution while solving the generated linear system through the approximation equation iteratively. In our study, we apply the preconditioning technique to construct a preconditioned linear system which eventually derives into a Full-Sweep Preconditioned AOR. From the presented results, we show that the proposed Full-Sweep Preconditioned AOR iterative method has superiority in efficiency compared to the basic Full-Sweep Preconditioned SOR and Full-Sweep Preconditioned Gauss-Seidel iterative methods.

Preconditioned tensor splitting AOR iterative methods for ℋ‐tensor equations

SummaryBased on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) ‐tensors. In this article, we introduce H‐splitting and H‐compatible splitting and investigate the relationship between these different splittings and their convergence. Meanwhile, we also consider a preconditioned AOR iterative method for solving tensor equations with nonsingular ‐tensors. We prove its convergence and give a comparison result on the spectral radius of the iteration tensor for the case when is a nonsingular ‐tensor. Numerical examples are also given to illustrate our methods.

Correction to: On the preconditioned AOR iterative method for Z-matrices

Correction to: On the preconditioned AOR iterative method for Z-matrices

On the preconditioned AOR iterative method for Z-matrices

In this paper, considering a general class of preconditioners \(P(\alpha )\), we study the convergence properties of the preconditioned AOR (PAOR) iterative methods for solving linear system of equations. It is shown that the spectral radius of the iteration matrix of the PAOR method has a monotonically decreasing property when the value of \(\alpha \) increases.

A Preconditioned AOR Iterative Method for an H-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.

Convergence of the Preconditioned AOR Method for an H-Matrix

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.

Multi-level preconditioned block accelerated overrelaxation iteration method for z-matrices

A class of multi-level preconditioners and corresponding preconditioned block AOR iterative method are presented and studied in this paper. We analyze the convergence performance of the new method and give the comparison theorems for different preconditioning level. Numerical results further verify our theoretical analysis and show that the proposed method has faster convergence speed than existing preconditioned block AOR method.

On the Preconditioning of the AOR Iterative Methods for M-matrices

In this paper, we propose a preconditioned AOR iterative method for solving the systems of linear equations with M-matrix coefficient. Some numerical results are given to compare the proposed preconditioner with an available preconditioner.

New preconditioned AOR iterative method for Z-matrices

In this paper, we present a new preconditioned AOR-type iterative method for solving the linear system Ax=b, where A is a Z-matrix, and prove its convergence. Then we give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method. Finally, we give two numerical examples to illustrate our results.

Convergence Analysis of Preconditioned AOR Iterative Method for Linear Systems

M-(H-)matrices appear in many areas of science and engineering, for example, in the solution of the linear complementarity problem (LCP) in optimization theory and in the solution of large systems for real-time changes of data in fluid analysis in car industry. Classical (stationary) iterative methods used for the solution of linear systems have been shown to convergence for this class of matrices. In this paper, we present some comparison theorems on the preconditioned AOR iterative method for solving the linear system. Comparison results show that the rate of convergence of the preconditioned iterative method is faster than the rate of convergence of the classical iterative method. Meanwhile, we apply the preconditioner toH-matrices and obtain the convergence result. Numerical examples are given to illustrate our results.

A new preconditioned AOR iterative method for [formula omitted]-matrices

Li et al. [Y.T. Li, C. Li, S. Wu, Improvements of preconditioned AOR iterative methods for L -matrices, J. Comput. Appl. Math. 206 (2007) 656–665] have considered the modified AOR method with a preconditioner ( I + S α ). In this paper, we present a new preconditioner ( I + S α β ) instead of ( I + S α ). The comparison theorems and numerical experiments show that the proposed new method can achieve faster convergence than the preconditioner introduced by Li et al.

A multi-parameters preconditioned AOR iterative method for linear systems

In order to improve the convergence rates of iterative method solving the linear system Ax = b , a preconditioned AOR iterative method with a multi-parameters preconditioner I + S ∼ α is proposed. Some convergence and comparison results for α i ∈ [ 0 , 1 ] are given when A is an L-matrix. When A is an H-matrix, the convergence of the corresponding methods is discussed for α i ∈ [ 0 , α i ′ ) , where α i > 1 . Furthermore, effectiveness of the new preconditioner method is shown by numerical experiments. Numerical experiments show that our methods are superior to the basic AOR iterative methods.

A modified AOR-type iterative method for L-matrix linear systems

AbstractBoth Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the preconditioned Gauss-Seidel method is faster than that of the preconditioned AOR iterative method.

A note on preconditioned AOR method for [formula omitted]-matrices

In this note, some errors in a recent article by Li et al. (Improvements of preconditioned AOR iterative methods for L -matrices, J. Comput. Appl. Math. 206 (2007) 656–665) are pointed out and some correct results are presented.

Improvements of preconditioned AOR iterative method for L-matrices

In this paper, we improve the preconditioned AOR method of linear systems considered by Evans et al. [The AOR iterative method for new preconditioned linear systems, Comput. Appl. Math. 132 (2001) 461–466]. In Evans’ paper, the coefficient matrix of linear system have to be an L-matrix with a i , i + 1 a i + 1 , i > 0 , i = 1 , … , n - 1 and 0 < a 1 n a n 1 < 1 . When a i , i + 1 a i + 1 , i = 0 for some i ∈ N = { 1 , … , n - 1 } , the preconditioned method is invalid. In order to solve the above problem, a new preconditioner is presented. Meanwhile, some recent results are improved.

Preconditioned AOR iterative method for linear systems

For solving the linear system A x = b , different preconditioned Gauss–Seidel methods have been proposed by many authors. In this paper, we will present preconditioned AOR iterative methods with two different preconditioners, and give corresponding convergence and comparison results. Numerical example is also given to illustrate our results.

Preconditioned Aor Iterative Methods for Linear Systems

In this paper we present the comparison analysis between preconditioned AOR method and AOR method under wider conditions than those in recent papers. Some numerical examples are given to illustrate our assertion.