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

New algorithm for solving pentadiagonal CUPL-Toeplitz linear systems

“…is the euclidean vector norm. The compared results between our algorithm and algorithme [12], algorithme [14] and MATLAB Solver for all tests examples are presented in Tables 2-6. For all numerical tests, we can see that our algorithm takes less CPU time and is about twice as fast as other algorithms.…”

“…The compared results, absolute errors x − x * , residuals Ax − f , and CPU time between our algorithm and algorithme [12], algorithme [14] and MATLAB Solver are presented in Table 7. We can see that our proposed algorithm takes less CPU time and is about twice faster than the algorithme [12], algorithme [14] and MATLAB Solver.…”

“…Remark 1. In step 1 of the algorithm presented in [12], we used fast pentadiagonal Toeplitz solver and MATLAB Solver, is a solver for pentadiagonal linear system from MATLAB.…”

“…In this paper we have exploited the special pentadiagonal CUPL-Toeplitz structure to develop a fast algorithm for solving pentadiagonal CUPL-Toeplitz linear systems. We compare our algorithm with the algorithms [12], [14] and MATLAB Solver, the numerical results show that our algorithm is more efficient, in terms of time, almost half that of the other algorithms and in terms of error.…”

“…For calculating the inverse of CUPL-Toeplitz matrix, an explicit inverses of this matrix were introduced [11]. Recently, based on the decomposition form a CUPL-Toeplitz matrix (2) and the Sherman-Morrison-Woodbury formula, Fu et al [12] presented two algorithms to solve the CUPL-Toeplitz linear system…”