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

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 $sep_F(A,B)$.

• Keywords

@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} }