| 对称三对角矩阵的QL方法论 |
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| 引用本文： | 蒋尔雄.对称三对角矩阵的QL方法论[J].上海大学学报(英文版),2004,8(4):369-377. |
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| 作者姓名： | 蒋尔雄 |
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| 作者单位： | DepartmentofMathematics,CollegeofSciences,ShanghaiUniversity,Shanghai200436,P.R.China |
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| 基金项目： | ProjectsupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .197710 2 0 ) |
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| 摘 要： | QL(QR) method is an efficient method to find eigenvalues of a matrix. Especially we use QL(QR) method to find eigenvalues of a symmetric tridiagonal matrix. In this case it only costs O( n^2) flops, to find all eigenvalues. So it is one of the most efficient method for symmetric tridiagonal matrices. Many experts have researched it. Even the method is mature, it still has many problems need to be researched. We put forward five problems here. They are: (1) Convergence and convergence rate; (2) The convergence of diagonal elements; (3) Shift designed to produce the eigenvalues in monotone order; (4) QL algorithm with multi-shift; (5) Error bound. We intoduce our works on these problems, some of them were published and some are new.
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| 关 键 词： | QL算法 对称三对角矩阵 矩阵特征值问题 误差边界 |
| 收稿时间： | 1 December 2003 |
QL method for symmetric tridiagonal matrices |
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| Jiang?Er-xiong.QL method for symmetric tridiagonal matrices[J].Journal of Shanghai University(English Edition),2004,8(4):369-377. |
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| Authors: | Jiang Er-xiong |
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| Institution: | Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200436, P. R. China |
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| Abstract: | QL(QR) method is an efficient method to find eigenvalues of a matrix. Especially we use QL(QR) method to find eigenvalues of a symmetric tridiagonal matrix. In this case it only costs O(n2) flops, to find all eigenvalues. So it is one of the most efficient method for symmetric tridiagonal matrices. Many experts have researched it. Even the method is mature, it still has many problems need to be researched. We put forward five problems here. They are: (1) Convergence and convergence rate; (2) The convergence of diagonal elements; (3) Shift designed to produce the eigenvalues in monotone order; (4) QL algorithm with multi-shift; (5) Error bound. We intoduce our works on these problems, some of them were published and some are new. |
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| Keywords: | matrix eigenvalue problem symmetric tridiagonal matrix QL(QR) algorithm shift error bound |
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