Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the add...Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.展开更多
在传统的LMS(Least Mean Square)算法中,固定步长的选取影响收敛速度与稳态误差,而且两者不可兼得。因此,为在相应的领域内合理使用此类算法,针对这个问题在对多种自适应滤波LMS类算法进行原理分析后,得出此类算法在不同领域的特点,对...在传统的LMS(Least Mean Square)算法中,固定步长的选取影响收敛速度与稳态误差,而且两者不可兼得。因此,为在相应的领域内合理使用此类算法,针对这个问题在对多种自适应滤波LMS类算法进行原理分析后,得出此类算法在不同领域的特点,对今后不同人群的合理使用提供了良好条件。展开更多
基金supported by the National Natural Science Foundation of China (No. 10671154)the Na-tional Basic Research Program (No. 2005CB321703)the Science and Technology Foundation of Guizhou Province of China (No. [2008]2123)
文摘Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.