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$\left(n\log n\right)$ 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.

中文翻译：

---

从马尔可夫链中找到CUPL-Toeplitz线性系统解的快速算法

本文解决了马尔可夫链的非奇异CUPL-Toeplitz线性系统。我们介绍了两种快速方法，其复杂度可以认为是O$（ñ\mathrm{日志}ñ）$基于CUPL-Toeplitz矩阵的分割方法，该方法等于Toeplitz矩阵减去秩一矩阵。最后，我们通过三个数值实验确认了新算法的性能。