A Robust Distributed Algorithm For Solving Linear Algebraic Equations

Linear algebraic equations have been widely applied in various regions such as structural analysis,economic model simulation,chemical engineering and electronic engineering.There is no central processing unit in the sensor network and network location problems.Each sensor can only grasp the local information of the system,and collaborate with others to achieve the overall system goal.The corresponding mathematical model in this case is equivalent to finding a common solution of the multiple linear algebraic equations in distributed computing environment.Therefore,it is of great practical significance to study the distributed algorithm for solving linear algebraic equations.DALE is a distributed algorithm for solving linear algebraic equations via multi-agent system.Each agent in the system corresponds to a linear algebraic equations.When there are common solutions to the multiple equations,the algorithm can find a solution of the equations corresponding to the integrated system.In this paper,considering that the equations corresponding to the integrated system does not necessarily have solutions,we improve the DALE and propose a robust distributed algorithm.The nonhomogeneous linear algebraic equations is transformed into homogeneous linear algebraic equations,then the solution of the non-homogeneous linear algebraic equations is obtained by solving the homogeneous linear algebraic equations.The new method has more concise form of iteration formula and improves the numerical performance of the algorithm.Global convergence of the iterative sequences generated by the new method is established.At the same time,by increasing the stopping criteria,the new method can avoid sinking into dead circulation for the equations without solution.The numerical results are also presented to show the efficiency and robustness of the proposed algorithm.