This paper introduces some efficient initials for a well-known algorithm （an inverse iteration） for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algori...This paper introduces some efficient initials for a well-known algorithm （an inverse iteration） for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also unexpectedly efficient. The initials presented here are based on our analytic estimates of the maximal eigenvalue and a mimic of its eigenvector for many years of accumulation in the study of stochastic stability speed. In parallel, the same problem for computing the next to the maximal eigenpair is also studied.展开更多
基金Acknowledgements The main results of the paper have been reported at Anhui Normal University, Jiangsu Normal University, the International Workshop on SDEs and Numerical Methods at Shanghai Normal University, Workshop on Markov Processes and Their Applications at Hunan University of Arts and Science, and Workshop of Probability Theory with Applications at University of Macao. The author acknowledges Professors Dong-Jin Zhu, Wan-Ding Ding, Ying-Chao Xie, Xue-Rong Mao, Xiang-Qun Yang, Xu-Yan Xiang, Jie Xiong, Li-Hu Xu, and their teams for very warm hospitality and financial support. The author also thanks Ms. Yue-Shuang Li for her assistance in computing large matrices. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11131003）, the ＂985＂ project from the Ministry of Education in China, and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘This paper introduces some efficient initials for a well-known algorithm （an inverse iteration） for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also unexpectedly efficient. The initials presented here are based on our analytic estimates of the maximal eigenvalue and a mimic of its eigenvector for many years of accumulation in the study of stochastic stability speed. In parallel, the same problem for computing the next to the maximal eigenpair is also studied.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.90412006No.90412011+7 种基金No.60573110No.90612016 No.60673152)国家高技术研究发展计划(863)(the National High- Tech Research and Development Plan of China under Grant No. 2006AA01A101No.2006AA01A108No.2006AA01A111)国家重点基础研究发展规划(973)(the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318000No.2003CB317007)。
