Fast and Scalable Parallel Algorithms for Matrix Chain Product and Matrix Powers on Reconfigurable Pipelined Optical Buses

Given N matrices A1, A2, ..., AN of size N × N, the matrix chain product problem is to compute A1 × A2 × ...× AN. Given an N × N matrix A, the matrix powers problem is to calculate the first N powers of A, i.e., A, A, A, ..., A. Both problems are important in conducting many matrix manipulations such as computing the characteristic polynomial, determinant, rank, and inverse of a matrix, and in general scientific computations. Both problems can be solved by using a matrix multiplication algorithm as a subroutine. Assume that the fastest sequential matrix multiplication algorithm has time complexity O(N), where the current best value of α is less than 2.3755 [3]. Then, sequentially, both the matrix chain product and the matrix powers problems can be solved in O(N) time. It is clear that for parallel computation of these two problems, a fast and scalable parallel matrix multiplication algorithm is required. Recently, we developed a paral-