An Effcient and Stable Structure Preserving Algorithm for Computing the Eigenvalues of a Hamiltonian Matrix

YAN Qing-you; XIONG Xi-wen

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YAN Qing-you, XIONG Xi-wen. An Effcient and Stable Structure Preserving Algorithm for Computing the Eigenvalues of a Hamiltonian Matrix[J]. Applied Mathematics and Mechanics, 2002, 23(11): 1150-1168.

Citation:

YAN Qing-you, XIONG Xi-wen. An Effcient and Stable Structure Preserving Algorithm for Computing the Eigenvalues of a Hamiltonian Matrix[J]. Applied Mathematics and Mechanics, 2002, 23(11): 1150-1168.

Citation:

YAN Qing-you, XIONG Xi-wen. An Effcient and Stable Structure Preserving Algorithm for Computing the Eigenvalues of a Hamiltonian Matrix[J]. Applied Mathematics and Mechanics, 2002, 23(11): 1150-1168.

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An Effcient 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 Date: 2001-02-27
Rev Recd Date: 2002-06-28
Publish Date: 2002-11-15

Abstract

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 socalled 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.
- Hamiltonian matrix,
- QR like algorihm,
- eigenvalue,
- stability,
- dis-unstabilization,
- backtrack technique,
- ratio-reduction

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References(19)

References

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