Fast algorithms for finding the solution of CUPL-Toeplitz linear system from Markov chain

Abstract

In this paper, the nonsingular CUPL-Toeplitz linear system from Markov chain is solved. We introduce two fast approaches whose complexity could be considered to be O(nlogn) based on the splitting method of the CUPL-Toeplitz matrix which equals to a Toeplitz matrix minus a rank-one matrix. Finally, we confirm the performance of the new algorithms by three numerical experiments.