数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 1189-1202.doi: 10.1016/S0252-9602(11)60309-3

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A NEW ALGORITHM FOR COMPUTING LARGEST REAL PART EIGENVALUE OF MATRICES: COLLATZ &|PERRON-FROBERNIUS&rsquo|APPROACH

Tedja Santanoe Oepomo   

  1. Science, Technology, Engineering, and Mathematics Division, Los Angeles Harbor/West LA Colleges, National University, and California International University, 1301Las Riendas Drive Units: 15, Las Habra, CA 90631, U.S.A.
  • 收稿日期:2008-04-07 修回日期:2010-02-23 出版日期:2011-05-20 发布日期:2011-05-20

A NEW ALGORITHM FOR COMPUTING LARGEST REAL PART EIGENVALUE OF MATRICES: COLLATZ &|PERRON-FROBERNIUS&rsquo|APPROACH

Tedja Santanoe Oepomo   

  1. Science, Technology, Engineering, and Mathematics Division, Los Angeles Harbor/West LA Colleges, National University, and California International University, 1301Las Riendas Drive Units: 15, Las Habra, CA 90631, U.S.A.
  • Received:2008-04-07 Revised:2010-02-23 Online:2011-05-20 Published:2011-05-20

摘要:

This paper describes a new method and algorithm for the numerical solution of eigenvalues with the largest real part of positive matrices. The method is based on a numerical implementation of Collatz’s eigenvalue inclusion theorem for non-negative irre-ducible matrices. Eigenvalues are analyzed for the studies of the stability of linear systems. Finally, a numerical discussion is given to derive the required number of mathematical op-erations of the new algorithm. Comparisons between the new algorithm and several well known ones, such as Power, and QR methods, are discussed.

关键词: Collatz’s theorem, Perron-Frobernius theorem, eigenvalue

Abstract:

This paper describes a new method and algorithm for the numerical solution of eigenvalues with the largest real part of positive matrices. The method is based on a numerical implementation of Collatz’s eigenvalue inclusion theorem for non-negative irre-ducible matrices. Eigenvalues are analyzed for the studies of the stability of linear systems. Finally, a numerical discussion is given to derive the required number of mathematical op-erations of the new algorithm. Comparisons between the new algorithm and several well known ones, such as Power, and QR methods, are discussed.

Key words: Collatz’s theorem, Perron-Frobernius theorem, eigenvalue

中图分类号: 

  • 15A48