AN EFFICIENT AND STABLE STRUCTURE PRESERVING ALGORITHM FOR COMPUTING THE EIGENVALUES OF A HAMILTONIAN MATRIX

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (11): 1292-1309.

AN EFFICIENT AND STABLE STRUCTURE PRESERVING ALGORITHM FOR COMPUTING THE EIGENVALUES OF A HAMILTONIAN MATRIX

闫庆友^1,2, 熊西文¹

1. Center of Advanced Design Technology, Dalian University, Dalian 116622, P. R. China;
2. Department of Economics and Statistics, Shandong Finance Institute, Jinan 250014, P. R. China

收稿日期:2001-02-27 修回日期:2002-06-08 出版日期:2002-11-18 发布日期:2002-11-18
基金资助:
the Special Funds for the State Major Basic Research Projects(G1999032805);the Foundation for Excellent Young Scholars by the Ministry of Education;the Research Fund for the Doctoral Program of Higher Education and the Foundation for Key Scholars in Chinese Universities

AN EFFICIENT AND STABLE STRUCTURE PRESERVING ALGORITHM FOR COMPUTING THE EIGENVALUES OF A HAMILTONIAN MATRIX

YAN Qing-you^1,2, XIONG Xi-wen¹

1. Center of Advanced Design Technology, Dalian University, Dalian 116622, P. R. China;
2. Department of Economics and Statistics, Shandong Finance Institute, Jinan 250014, P. R. China

Received:2001-02-27 Revised:2002-06-08 Online:2002-11-18 Published:2002-11-18
Supported by:
the Special Funds for the State Major Basic Research Projects(G1999032805);the Foundation for Excellent Young Scholars by the Ministry of Education;the Research Fund for the Doctoral Program of Higher Education and the Foundation for Key Scholars in Chinese Universities

摘要/Abstract

摘要： An efficient and stable structure preserving algorithm, which is a variant of the QR like (SR) algorithm due to Bunse-Gerstner and Mehrmann, is presented for computing the eigenvalues and stable invariant subspaces of a Hamiltonian matrix In the algorithm two strategies are employed, one of which is called dis-unstabilization technique and the other is preprocessing technique Together with them, a so-called ratio-reduction equation and a backtrack technique are introduced to avoid the instability and breakdown in the original algorithm It is shown that the new algorithm can overcome the instability and breakdown at low cost Numerical results have demonstrated that the algorithm is stable and can compute the eigenvalues to very high accuracy.

关键词: Hamiltonian matrix, QR like algorithm, eigenvalue, stability, dis-unstabilization, backtrack technique, ratio-reduction

Abstract: An efficient and stable structure preserving algorithm, which is a variant of the QR like (SR) algorithm due to Bunse-Gerstner and Mehrmann, is presented for computing the eigenvalues and stable invariant subspaces of a Hamiltonian matrix In the algorithm two strategies are employed, one of which is called dis-unstabilization technique and the other is preprocessing technique Together with them, a so-called ratio-reduction equation and a backtrack technique are introduced to avoid the instability and breakdown in the original algorithm It is shown that the new algorithm can overcome the instability and breakdown at low cost Numerical results have demonstrated that the algorithm is stable and can compute the eigenvalues to very high accuracy.

Key words: Hamiltonian matrix, QR like algorithm, eigenvalue, stability, dis-unstabilization, backtrack technique, ratio-reduction

中图分类号:

O241.6

闫庆友;熊西文. AN EFFICIENT AND STABLE STRUCTURE PRESERVING ALGORITHM FOR COMPUTING THE EIGENVALUES OF A HAMILTONIAN MATRIX[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(11): 1292-1309.

YAN Qing-you;XIONG Xi-wen. AN EFFICIENT AND STABLE STRUCTURE PRESERVING ALGORITHM FOR COMPUTING THE EIGENVALUES OF A HAMILTONIAN MATRIX[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(11): 1292-1309.

参考文献

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AN EFFICIENT AND STABLE STRUCTURE PRESERVING ALGORITHM FOR COMPUTING THE EIGENVALUES OF A HAMILTONIAN MATRIX

AN EFFICIENT AND STABLE STRUCTURE PRESERVING ALGORITHM FOR COMPUTING THE EIGENVALUES OF A HAMILTONIAN MATRIX

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