Preconditioned AOR Research Articles

A new preconditioned AOR method for solving multi-linear systems

In this paper, a new preconditioned AOR method for solving the multi-linear systems with -tensor is presented. The convergence of the new method and the corresponding comparison for the spectral radius of preconditioned iterative tensors are given. Numerical examples demonstrate that the new method is feasible and effective. As an application, we also show the efficiency of our preconditioner for solving higher order Markov chains.

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.

Computational algorithm PAOR for time-fractional diffusion equations

We deal with the application of an unconditionally implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations (TFDE’s) via the Caputo’s time fractional derivative. Based on this implicit approximation equation, the corresponding linear system can be generated in which its coefficient matrix is large scale and sparse. To speed up the convergence rate in solving the linear system iteratively, we construct the corresponding preconditioned linear system. Then we formulate and implement the Preconditioned AOR (PAOR) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of PAOR method. The numerical results of this study show that the proposed iterative method is superior to PSOR and PGS, GS iterative method.

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.

Comparison results of the preconditioned AOR methods for L-matrices

In this paper, we first provide comparison results of several types of the preconditioned AOR (PAOR) methods for solving a linear system whose coefficient matrix is an L-matrix satisfying some weaker conditions than those used in the recent literature. Next, we propose an application of PAOR method to a preconditioner of Krylov subspace method. Lastly, numerical results are provided to show that Krylov subspace method with the PAOR preconditioner performs quite well as compared with the ILU (0) preconditioner.

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.

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 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 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.