A Fast Algorithm for Evaluating the m-th Power of Level Circulant Matrices of Type

It is well known that the circulant matrices are very important and special matrix. In recent years, various type of circulant matrices have been applied in such as signal dealing and oil exploration, and so on. In this paper, motivated by [Shen Guangxing (2004)], we give a fast algorithm for evaluating the m-th power of level-k(r₁, r₂, ···, r_k)-circulant matrices of type (n₁, n₂, ···, n_k). By [Shen Guangxing (2004)], and [Lu Chengbo (2004)], we can see the complexity of computation can reduce n times.