  It is well-known that a multilinear system with a nonsingular M-tensor and a
positive right-hand side has a unique positive solution. Tensor splitting
methods generalizing the classical iterative methods for linear systems have
been proposed for finding the unique positive solution. The Alternating
Anderson-Richardson (AAR) method is an effective method to accelerate the
classical iterative methods. In this study, we apply the idea of AAR for
finding the unique positive solution quickly. We first present a tensor
Richardson method based on tensor regular splittings, then apply Anderson
acceleration to the tensor Richardson method and derive a tensor
Anderson-Richardson method, finally, we periodically employ the tensor
Anderson-Richardson method within the tensor Richardson method and propose a
tensor AAR method. Numerical experiments show that the proposed method is
effective in accelerating tensor splitting methods.
