带有纯放大环节的方线性系统的稳定解耦

本文利用Ｙｏｋｏｙａｍａ标准形与系统传递函数阵间的直接对应关系,用构造性方法给出了带纯放大环节的方线性系统稳定解耦问题有解的充分必要条件。当条件满足时,问题的解是容易给出的。     

A PRODUCT HYBRID GMRES ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES(m) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algorithms for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one.