求解BTTB系统的迭代算法

The Iterative Algorithm for Block-Toeplitz-Toeplitz-Block Systems

BTTB矩阵在信号处理等工程问题中有着广泛的应用,因此,针对这种类型矩阵的特点,利用它们的结构来设计一些数值稳定的、收敛性能好的快速算法,具有极为重要的意义.文章讨论了块三角Toeplitz矩阵的一些性质,给出了求解块下三角Toeplitz矩阵逆的快速算法,并对其复杂性进行了分析.利用这种求逆算法进而给出了求解BTTB系统的块Gauss-Seidel迭代算法和块SOR迭代算法,并讨论了其收敛性.数值实验得到验证.

BTYB matrices have a wide range of engineering applications such as in signal processing. In view of the charac- teristics of this type of matrix, it is very significant that we design some fast algorithms with numerical stability and the good property of convergence. Firstly, we discussed some properties of block triangular Toeplitz matrices, then we presented fast algorithms for computing the inverse of such a class of matrices and also analyzed the complexity of this algorithm. Using the inverse algorithm, we gave Block-Gauss-Seidel iteration algorithm and Block-SOR iteration algorithm for solving the BTTB system.