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New Algorithm for the Computation of the Smallest Eigenvalue of a SymmetricMatrix and Its Eigenspace

机译：计算对称矩阵及其特征空间最小特征值的新算法

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摘要

The problem of finding the smallest eigenvalue and the corresponding eigenspaceof a symmetric matrix is stated as a semidefinite optimization problem. A straightforward application of nowadays more or less standard routines for the solution of semidefinite problems yields a new algorithm for the smallest eigenvalue problem; the approach not only yields the smallest eigenvalue, but also a symmetric positive semidefinite (SPSD) matrix whose column space is equal to the eigenspace for the smallest eigenvalue. It is shown that the predictor-corrector method yields a polynomial time algorithm which, with a suitable choice of the step size, asymptotically is quadratically convergent.

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作者
Jansen, B.; Roos, C.; Terlaky, T.;
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年度 1995
页码 p.1-22
总页数 22
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Eigenvalues; Matrices(Mathematics); Applied mathematics;

机译：特征值;矩阵（数学）;应用数学;

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1. An eigenspace method for computing derivatives of semi-simple eigenvalues and corresponding eigenvectors of quadratic eigenvalue problems [J] . Xin Lu, Shu-fang Xu Applied numerical mathematics . 2015,第auga期

机译：计算二次特征值问题的半简单特征值导数和相应特征向量的特征空间方法
2. Sub-gradient algorithms for computation of extreme eigenvalues of a real symmetric matrix [J] . Adnan Yassine Control and Cybernetics . 1998,第3期

机译：计算实对称矩阵极值特征的次梯度算法
3. LARGEST EIGENVALUE OF THE LAPLACIAN MATRIX: ITS EIGENSPACE AND TRANSITIVE ORIENTATIONS [J] . Iriarte Benjamin SIAM Journal on Discrete Mathematics . 2016,第4期

机译：拉普拉斯矩阵的最大特征值：其特征空间和过渡方向
4. Numerical Computation Studies between a New Algorithm, Power, and QR Iterative Algorithms for Solution of Eigenvalue of Essentially Positive Matrices [C] . Tedja Santanoe Oepomo International conference on management science and engineering management . 2013

机译：新算法，功率和QR迭代算法的数值计算研究，用于基本上正矩阵的特征值
5. Algorithms for Large Scale Problems in Eigenvalue and SVD Computations and in Big Data Applications. [D] . Wu, Lingfei. 2016

机译：特征值和SVD计算以及大数据应用中的大规模问题的算法。
6. Adaptive Morley element algorithms for the biharmonic eigenvalue problem [O] . Hao Li, Yidu Yang -1

机译：双调和特征值问题的自适应Morley元素算法
7. Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software [O] . Bo Kågström, Peter Poromaa 1994

机译：用规则矩阵对（a，B）的特定特征值计算特征空间和条件估计：理论，算法和软件

New Algorithm for the Computation of the Smallest Eigenvalue of a SymmetricMatrix and Its Eigenspace

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