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Volume 2, Issue 3
Estimation of the Separation of Two Matrices

Ji-Guang Sun

J. Comp. Math., 2 (1984), pp. 189-200.

Published online: 1984-02

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  • Abstract

The estimation of the solution to the matrix equation AX-XB=C is primarily dependent on the quantity sep(A,B) introduced by Stewart. Varah has given some examples to show that $sep_F(A,B)$ can be very small even though the eigenvalues of A and B are well separated. In this paper we give some lower bounds of $sep_F(A,B)$.

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@Article{JCM-2-189, author = {Ji-Guang Sun}, title = {Estimation of the Separation of Two Matrices}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {3}, pages = {189--200}, abstract = {

The estimation of the solution to the matrix equation AX-XB=C is primarily dependent on the quantity sep(A,B) introduced by Stewart. Varah has given some examples to show that $sep_F(A,B)$ can be very small even though the eigenvalues of A and B are well separated. In this paper we give some lower bounds of $sep_F(A,B)$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9653.html} }
TY - JOUR T1 - Estimation of the Separation of Two Matrices AU - Ji-Guang Sun JO - Journal of Computational Mathematics VL - 3 SP - 189 EP - 200 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9653.html KW - AB -

The estimation of the solution to the matrix equation AX-XB=C is primarily dependent on the quantity sep(A,B) introduced by Stewart. Varah has given some examples to show that $sep_F(A,B)$ can be very small even though the eigenvalues of A and B are well separated. In this paper we give some lower bounds of $sep_F(A,B)$.

Ji-Guang Sun. (1984). Estimation of the Separation of Two Matrices. Journal of Computational Mathematics. 2 (3). 189-200. doi:
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