We provide a novel recursive method, which does not require any assumption, to compute the entries of the kth power of a semicirculant matrix by using a closed-form expression for the mth term of a certain recursive polynomial sequence. As an application, a method for computing the entries of the kth power of r-circulant matrices is also presented.

中文翻译：

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半循环矩阵和 r 循环矩阵的任意正幂

我们提供了一种不需要任何假设的新颖递归方法，通过使用某个递归多项式序列的第 m项的封闭形式表达式来计算半循环矩阵的k次方的项。作为一个应用，还给出了一种计算r循环矩阵的k次方项的方法。