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

A tensor Alternating Anderson-Richardson method for solving multilinear systems with M-tensors