An algorithm for multiplying a chain of Kronecker products by a matrix is described. The algorithm does not require that the Kronecker chain actually be computed and the main computational work is a series of matrix-matrix multiplications. Use of the algorithm can lead to substantial savings in both memory requirements and computational speed. Although similar algorithms have been described before, this article makes two novel contributions. First, it shows how shuffling of data can be (largely) avoided. Second, it provides a simple method to determine the optimal ordering of the workflow.
