An Acceleration Algorithm For Solving Multi-linear Systems

Multi-linear systems often appear in many fields of scientific and engineering.Recently,many algorithms have been proposed for solving multi-linear systems with ?-tenors,which can be divided two types.The first is tensor splitting methods,the second is tensor type methods.There are a series of algorithms that apply Anderson acceleration to the classical iterations in linear systems,whose convergence perform better.Since 2-order tensors are matrices,we try to apply Anderson acceleration to accelerate the convergence of the tensor splitting method with regular splitting.In this paper,we extend the Alternating Anderson-Richardson(AAR)algorithm for solving multi-linear systems with ?-tenors and positive right-hand sides.Firstly,give the Richardson iteration.Then,propose the Anderson Richardson(AR)iteration by defining the correction residuals.Finally,we apply AR iteration periodically to accelerate the convergence of Richardson iteration.Furthermore,we give a way to select the relaxation parameters,and choose the appropriate parameters by numerical experiments.Numerical experiments show the effectiveness of this algorithm.