M. T. Chu (2000), `A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values', SIAM J. Numer. Anal. 37, 1004-1020 (electronic). Home/Search Document Not in Database Summary Related Articles Check |
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Construction of Matrices With Prescribed Singular Values and .. - Chi-Kwong Li And (Correct)
....so that the last n Gamma r diagonal entries are in ascending order. Set r = r 1 and go to Step 1. 4 Real Matrices with Complex Eigenvalues Chu mentions that the construction of a real matrix with prescribed singular values and complex eigenvalues occuring in conjugate pairs is an open problem [4]. This is a a very natural question when constructing matrices to test numerical software. We provide a construction using a slight modification of the ideas in the previous section. Note that we are able to maintain a block triangular structure, and control the order of the eigenvalues appearing ....
....j; j m j; j 1 j; j r j lies in the interval h Q k j=1 s n Gammaj 1 ; Q k j=1 s j i . 10 5 Relation to other research Smoktunowicz and Aleksiejczyk showed how to construct an upper triangular matrix with singular values whose product is 1, and whose eigenvalues are all 1. Chu [4], independently of our work, showed how to construct a matrix with specified singular values and eigenvalues that satisfy (1.1) His algorithm produces a matrix that is permutation similar to a triangular matrix, however his algorithm does not allow one to specify the order of the eigenvalues on ....
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M.T. Chu, A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values, preprint.
Structured Inverse Eigenvalue Problems - Chu, Golub (2002) (5 citations) Self-citation (Chu) (Correct)
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M. T. Chu (2000), `A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values', SIAM J. Numer. Anal. 37, 1004-1020 (electronic).
SINGULAR VALUE REASSIGNMENT WITH LOW RANK MATRICES (DRAFT.. - Delin Chu And Self-citation (Chu) (Correct)
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M. T. Chu, A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values, SIAM J. Numer. Anal., 37(2000), 1004-1020.
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