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2003, 04, 11-14
实对称矩阵的秩1修正的特征反问题
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摘要:

文章研究了如下的特征值反问题:给定实对称矩阵A,求实向量u和实数p,使矩阵A+puuT具有预先指定的特征值{λi}ln。计论了解的存在性与唯一性,并给出了数值算法。

Abstract:

This paper deals with the following inverse eigenvalue problem: Given a real symmetric matrix A, find a vector u and a real number p, so that matrix A + puu T has prescribed eigenvalues The existence and uniqueness of the solution are discussed and the algorithm and some numerical examples given.

参考文献

[1] Golub C H. Some modified matrix eigenvaltie problem[J]. SIAM Review, 1973, 15: 318-314.

[2] Bunch J R, Nielsen C P, Sorensen D C. Rank-one modification of the symmetric eigenproblem[J]. Numer Math, 1978, 31-48.

[3] Dongarra J J, Sorensen D C. A fully parallel algorithm for the symmetic eigenvalue problem[J]. SIAM J Sci Stat Comput, 1987, 139-154.

[4] Bunch J R, Nielsen C P. Updating the singular value decomposition[J]. Numer Math, 1978, 31: 111-129.

[5] Parlett B N. The symmetric eigenvalue problem[M]. Englewood Cliffs: Prentice-Hall Inc, 1980.

[6] Householder A S. The theory of matrices in numerical analysis [M]. New York: Blaisdell Publishing Company, 1964.

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中图分类号:O241

引用信息:

[1]殷庆祥.实对称矩阵的秩1修正的特征反问题[J].南通工学院学报(自然科学版),2003(04):11-14.

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