AOR Method Research Articles

Agent Navigation based on Boundary Value Problem using Iterative Methods

This paper presents the simulation of numerical solutions to the navigational problem of an agent traveling safely in its environment. The approach is based on the numeric solutions of the boundary value problem (BVP) that generate harmonic potential fields through a differential equation whose gradient represents navigation routes to the destination. Two methods, namely KSOR and KAOR, were tested to solve the BVP. KSOR and KAOR are variants of the standard SOR and AOR methods, respectively. In this work, the KSOR and KAOR methods were used to solve the BVP by applying Laplace's equation to obtain harmonic functions. The generated harmonic functions are then utilized by the searching algorithm to find a smooth navigational route for an agent to travel in its environment without colliding with any obstacles. The numerical results from the solutions of BVP demonstrate that the KAOR provides a faster execution time with fewer iterations compared to the KSOR method.

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.

Generalized interval AOR method for solving interval linear equations

Generalized interval AOR method for solving interval linear equations

An Improved Convergence Theorem of the Newton-Based AOR Method for Generalized Absolute Value Equations

For solving the large sparse generalized absolute value equations, recently a Newton-based accelerated over-relaxation (NAOR) method was investigated. In this paper, we widen the convergence regions for the parameters and establish a new convergence theorem of the NAOR method when the system matrix is an H+-matrix. Numerical examples demonstrate that the NAOR method has a better convergence performance when the parameters are taken according to the proposed convergence theorem.

Automated information support system for AOR methods of hazard and risk analysis for oil and gas industry

This article examines an attempt to formalize the procedures preceding the engineering methods of AOR, which allows experts to give the maximum of really significant information in a concise form and with a pronounced effect, freeing their limited resources from routine and search for insignificant versions of events to the detriment of the most important.

The modified Uzawa methods for solving singular linear systems

For nonsingular linear systems, Yun in 2013 studied three variants of the Uzawa method; see Yun (2013) [18]. These methods contain the Uzawa-AOR method and the Uzawa-SAOR method as special cases. On the basis of the Uzawa-AOR method and the Uzawa-SAOR method, Li in 2017 proposed two modified Uzawa methods by constructing the coefficient matrix of AOR method into a new form of the product of lower triangular matrix and upper triangular matrix; see Li (2017) [26]. In this paper, we present two modified Uzawa methods for solving singular linear systems. The semi-convergence of these methods is analyzed by using the techniques of singular value decomposition and Moore-Penrose inverse. The numerical results are used to verify the theoretical results.

On the generalized AOR and CG iteration methods for a class of block two-by-two linear systems

On the generalized AOR and CG iteration methods for a class of block two-by-two linear systems

An optimized AOR iterative method for solving absolute value equations

In recent years, the AOR iterative method has been proposed for solving absolute value equations. This method has two parameters ? and ?. In this paper, we intend to find the optimal parameters of this method to improve convergence rate by suitable optimization techniques. Meanwhile, the convergence of the optimized AOR iterative method is discussed. It is both theoretically and experimentally demonstrated efficiency of the optimized AOR iterative method in contrast with the AOR and SOR methods.

THE PRECONDITIONED GAOR METHODS FOR GENERALIZED LEAST SQUARES PROBLEMS

In this paper, we present some preconditioned generalized AOR (denoted by GAOR) methods for solving generalized least squares problems. We also compare the spectral radii of the iteration matrices of the proposed preconditioned and original methods. Finally, numerical experiments are provided to confirm the theoretical results.

On the Some New Preconditioned Generalized AOR Methods for Solving Weighted Linear Least Squares Problems

Recently, in the paper [Z.G. Huang, L.G. Wang, Z. Xu, J.J. Cui, Some new preconditioned generalized AOR methods for solving weighted linear least squares problems, Computational and Applied Mathematics, 37(2018) 415-438.], Huang et al, by using the generalized accelerated over-relaxation (GAOR) methods, proposed some new preconditioners for solving weighted linear least squares problems and discuss their comparison results. In this paper, we present a new model of GAOR methods to solve the weighted linear least squares problems. We prove that the new model is superior to the existing mentioned methods. Numerical examples are also reported to confirm our theoretical analysis.

Explicit group AOR method for solving elliptic partial differential equations

The explicit group overrelaxation methods for the numerical solution of the sparse linear systems derived from the discretisation of self-adjoint elliptic partial differential equations have been presented (Yousif & Evans, 1986) and has been shown to be computationally superior in comparison with the implicit 1-line and 2-line block succsessive overrelaxation (SOR) iterative methods. In this work a new explicit 4-point group accelerated overrelaxation (Group AOR) iterative method is presented. A comparison with the point AOR method for the model problem shows the computational advantages of the new technique.

The general inner-outer iteration method based on regular splittings for the PageRank problem

In this paper, combined the regular splittings of the coefficient matrix I−αP with the inner-outer iteration framework [9], a general inner-outer (GIO) iteration method is presented for solving the PageRank problem. Firstly, the AOR and modified AOR (MAOR) methods for solving the PageRank problem are constructed, and several comparison results are also given. Next, the GIO iteration scheme is developed, and its overall convergence is analyzed in detail. Furthermore, the preconditioner derived from the GIO iteration can be used to accelerate the Krylov subspace methods, such as GMRES method. Finally, some numerical experiments on several PageRank problems are provided to illustrate the efficiency of the proposed algorithm.

Generalized AOR method for solving a class of generalized saddle point problems

In this paper, by constructing appropriate splitting, a generalized AOR (GAOR) method for solving a class of generalized saddle point problems has been presented, and the convergence of the method is studied. The numerical experiments results show the efficiency and robustness of the new method.

The relaxation convergence of multisplitting AOR method for linear complementarity problem

In this paper, based on the previous work by Bai [On the convergence of the multisplitting methods for the linear complementarity problem. SIAM J Matrix Anal Appl. 1999;21:67–78] and by Zhang et al. [Improved convergence theorems of multisplitting methods for the linear complementarity problem. Appl Math Comput. 2014;243:982–987], we further discuss the multisplitting AOR (MAOR) method for the linear complementarity problem. Some new convergence conditions of the MAOR method are obtained, which are different from those of the aforementioned papers.

Path Planning in Structured Environment Using Harmonic Potentials via Half-Sweep Modified AOR Method

Path Planning in Structured Environment Using Harmonic Potentials via Half-Sweep Modified AOR Method

The improved convergence of MSMMAOR method for linear complementarity problems

In this paper, based on the previous work by Zhang and Li [The weaker convergence of modulus-based synchronous multisplitting multi-parameters methods for linear complementarity problems, Comput Math Appl. 2014;67:1954–1959], we further discuss the modulus-based synchronous multisplitting multi-parameters AOR (MSMMAOR) method for solving the linear complementarity problems. The new convergence conditions of the MSMMAOR method are obtained, which are weaker than those of the aforementioned paper.

A selected method for the optimal parameters of the AOR iteration

In this paper, we present an optimization technique to find the optimal parameters of the AOR iteration, which just needs to minimize the 2-norm of the residual vector and avoids solving the spectral radius of the iteration matrix of the SOR method. Meanwhile, numerical results are provided to indicate that the new method is more robust than the AOR method for larger intervals of the parameters ω and γ.

Some new preconditioned generalized AOR methods for solving weighted linear least squares problems

In this paper, we propose some new preconditioned GAOR methods for solving weighted linear least squares problems and discuss their comparison results. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Shen et al. (Appl Math Mech Engl Ed 33(3):375–384, 2012) and Wang et al. (J Appl Math, doi: 10.1155/2012/563586 , 2012) whenever these methods are convergent. Finally, numerical experiments are provided to confirm the theoretical results obtained in this paper.

Some new preconditioned generalized AOR methods for generalized least-squares problems

In this paper, we present some new preconditioned GAOR methods for solving generalized least-squares problems and their comparison results. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Zhou et al. (2009) [19] and Wang et al. (2013) [18] whenever these methods are convergent. Lastly, numerical experiments are provided to confirm the theoretical results.

Semi-convergence analysis of Uzawa–AOR method for singular saddle point problems

Based on AOR and Uzawa methods, this paper presents Uzawa–AOR method for solving a class of singular saddle point problems. We analyze its semi-convergence and the distribution of the eigenvalues of its iterative matrix. The theoretical results and effectiveness of the Uzawa–AOR method are supported by a numerical example.