解广义特征值反问题的同伦方法 |
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引用本文: | 夏又生.解广义特征值反问题的同伦方法[J].计算数学,1993,15(3):310-317. |
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作者姓名: | 夏又生 |
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作者单位: | 南京邮电学院数学教研室 |
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摘 要: | 1.引言 我们讨论下列广义特征值反问题: (G)已知B是n×n阶对称半正定矩阵,λ=(λ_1,…,λ_(2n-1))~T∈R~(2n-1),且{λ_i}~(n_3),和{λ_i}_(n+1)~(2n-1)严格交错。问题是欲求一个实对称三对角n×n阶矩阵A,使得λ_1…,λ_n是Ax=λBx的特征值,λ_(n+1),…,λ_(2n-1)是A_(n-1)x=λB_(n-1)x的特征值,其中A_(n-1),B_(n-1)分别是矩阵A,B的前n-1阶主子阵。
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关 键 词: | 特征值 反问题 广义 同伦法 |
A HOMOTOPY METHOD FOR SOLVING GENERALIZED INVERSE EIGENVALUE PROBLEMS |
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Institution: | Xia You-sheng Nanjing Institute of Posts and Telecommunications |
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Abstract: | In this paper, a homotopy method for solving generalized inverse eigenvalueproblems is proposed. It is shown that there are exactly n! (n-1)! distinct smoothcurves connecting trivial solutions to desired solutions for generalized inverse eig-envalue problems, some numerical examples are given. |
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