Efficient initials for computing maximal eigenpair

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• 作者：Mu-Fa Chen
• 关键词：Perron ; Frobenius theorem ; power iteration ; Rayleigh quotient iteration ; efficient initial ; tridiagonal matrix ; Q ; matrix
• 刊名：Frontiers of Mathematics in China
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：11
• 期：6
• 页码：1379-1418
• 全文大小：402 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576
• 卷排序：11

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.