A fast algorithm for solving tridiagonal quasi-Toeplitz linear systems

In this paper, we consider the solution of tridiagonal quasi-Toeplitz linear systems. By exploiting the special quasi-Toeplitz structure, we give a new decomposition form of the coefficient matrix. Based on this matrix decomposition form and combined with the Sherman-Morrison formula, we propose an efficient algorithm for solving the tridiagonal quasi-Toeplitz linear systems. Although our algorithm takes more floating-point operations (FLOPS) than the LU decomposition method, it needs less memory storage and data transmission and is about twice faster than the LU decomposition method. Numerical examples are given to illustrate the efficiency of our algorithm.