| 关于带Rayleigh商位移的QL方法 |
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| 引用本文： | 戴华.关于带Rayleigh商位移的QL方法[J].南京航空航天大学学报,1990(4). |
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| 作者姓名： | 戴华 |
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| 作者单位： | 南京航空学院数理力学系 |
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| 摘 要： | 本文讨论带Rayleigh商位移的QL方法的收敛性。给出了带Rayleigh商位移QL方法的收敛条件,并给出了带Rayleigh商位移QL方法不收敛的充分必要条件,证明了带Rayleigh商位移QL方法对任何不可约对称三对角矩阵总是有效的。
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| 关 键 词： | 线性代数计算法 对称矩阵 特征值 QL方法 Rayleigh商位移 |
On the QL Algorithm with Rayleigh Quotient Shift |
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| Dai Hua.On the QL Algorithm with Rayleigh Quotient Shift[J].Journal of Nanjing University of Aeronautics & Astronautics,1990(4). |
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| Authors: | Dai Hua |
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| Abstract: | In this paper, the convergence and non-convergence of the QL algorithm with the Rayleigh quotient shift (called RQL algorithm) are discussed. The sufficient condition for the convergence of the RQL algorithm is given. The sufficient and necessary conditions for the non-convergence of the RQL algorithm are established. It is shown that the RQL algorithm is always efficient for any irreducible, symmetric, and tridiagonal matrices. |
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| Keywords: | numerical algebra symmetric matrix eigenvalue QL algorithm Rayleigh quotient shift |
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