| 求解大规模非对称矩阵特征问题的精化双正交Lanczos算法 |
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| 引用本文： | 闫庆友,魏小鹏. 求解大规模非对称矩阵特征问题的精化双正交Lanczos算法[J]. 高等学校计算数学学报, 2004, 26(2): 110-124 |
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| 作者姓名： | 闫庆友 魏小鹏 |
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| 作者单位： | 山东财政学院经济统计系,济南,250014;华北电力大学工商管理学院,北京,102206;大连大学先进设计技术中心,大连,116622 |
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| 基金项目： | 国家自然科学基金资助(50275013,60174037) |
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| 摘 要： | We combine Lanczos algorithm with the thought of the refined projection method using QR factorization and propose the refined biothogonalization Lanczos method for computing the desired eigenvalues of large unsymmetric matrix. With low cost of work space and flops the algorithm cures the disease that the Ritz vectors may not converge when the Ritz values converge usingthe Lanczos method. Numerical experiments show our algorithm is considerably more stable and efficient than its counterpart.
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| 关 键 词： | 矩阵 精化双正交 正交投影 特征值 |
THE REFINED BIORTHOGONALIZATION LANCZOS ALGORITHM |
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| Yan Qingyou. THE REFINED BIORTHOGONALIZATION LANCZOS ALGORITHM[J]. Numerical Mathematics A Journal of Chinese Universities, 2004, 26(2): 110-124 |
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| Authors: | Yan Qingyou |
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| Abstract: | We combine Lanczos algorithm with the thought of the refined projection method using QR factorization and propose the refined biothogonalization Lanczos method for computing the desired eigenvalues of large unsymmetric matrix. With low cost of work space and flops the algorithm cures the disease that the Ritz vectors may not converge when the Ritz values converge using the Lanczos method. Numerical experiments show our algorithm is considerably more stable and efficient than its counterpart. |
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| Keywords: | refined biorthogonalization Lanczos algorithm refined approximate vectors orthogonal projection oblique projection Ritz values Ritz vectors. |
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