| ARNOLDI REDUCTION ALGORITHM FOR LARGE SCALE GYROSCOPIC EIGENVALUE PROBLEM |
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| 作者姓名： | Zheng Zhaochang Ren Gexue |
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| 作者单位： | Zheng Zhaochang;Ren Gexue，Department of Engineering Mechanics，Tsinghua University，Beijing 100084 |
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| 基金项目： | This research is supported by The National Science Foundation，The Doctoral Training Foundation |
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| 摘 要： | Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been devel-oped for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of systemmatrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm has been ob-tained, which is even simpler than the Lanczos algorithm for symmetric eigenvalue problems. Thecomplex number computation is completely avoided. A restart technique is used to enable the reductionalgorithm to have iterative characteristics. It has been found that the restart technique is not only ef-fective for the convergence of multiple eigenvalues but it also furnishes the reduction algorithm with atechnique to check and compute missed eigenvalues. By combining it with the restart technique, the al-gorithm is made practical for large-scale gyroscopic eigenvalue problems. Numerical examples are giv-en to demonstrate the effectiveness of the method proposed.
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| 收稿时间： | 20 January 1995 |
ARNOLDI REDUCTION ALGORITHM FOR LARGE SCALE GYROSCOPIC EIGENVALUE PROBLEM |
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| Zheng Zhaochang,Ren Gexue,.ARNOLDI REDUCTION ALGORITHM FOR LARGE SCALE GYROSCOPIC EIGENVALUE PROBLEM[J].Acta Mechanica Solida Sinica,1996,9(2):95-103. |
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| Authors: | Zheng Zhaochang Ren Gexue |
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| Institution: | (1) Department of Engineering Mechanics, Tsinghua University, 100084 Beijing |
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| Abstract: | Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been devel- oped for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm has been ob- tained, which is even simpler than the Lanczos algorithm for symmetric eigenvalue problems. The complex number computation is completely avoided. A restart technique is used to enable the reduction algorithm to have iterative characteristics. It has been found that the restart technique is not only ef- fective for the convergence of multiple eigenvalues but it also furnishes the reduction algorithm with a technique to check and compute missed eigenvalues. By combining it with the restart technique, the al- gorithm is made practical for large-scale gyroscopic eigenvalue problems. Numerical examples are giv- en to demonstrate the effectiveness of the method proposed. |
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| Keywords: | gyroscopic eigenvalue problem skew symmetry Arnoldi reduction algorithm restart technique |
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