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Volume 9, Issue 4
Extensions of the Kantorovich Inequality and the Bauer-Fike Inequality

Ji-Guang Sun

J. Comp. Math., 9 (1991), pp. 360-368.

Published online: 1991-09

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  • Abstract

This paper proves a Kantorovich-type inequality on the matrix of the type $\frac{1}{2}(Q^H_1 AQ_1 Q^H_1A^{-1} Q_1+Q^H_1A^{-1}Q_1Q^H_1AQ_1)$, where $A$ is an $n\times n$ positive definite Hermitian matrix and $Q_1$ is an $n\times m$ matrix with rank $(Q_1)=m$. The result is applied to get an extension of the Bauer-Fike inequality on condition numbers of similarities that block diagonalized matrices.

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@Article{JCM-9-360, author = {Sun , Ji-Guang}, title = {Extensions of the Kantorovich Inequality and the Bauer-Fike Inequality}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {4}, pages = {360--368}, abstract = {

This paper proves a Kantorovich-type inequality on the matrix of the type $\frac{1}{2}(Q^H_1 AQ_1 Q^H_1A^{-1} Q_1+Q^H_1A^{-1}Q_1Q^H_1AQ_1)$, where $A$ is an $n\times n$ positive definite Hermitian matrix and $Q_1$ is an $n\times m$ matrix with rank $(Q_1)=m$. The result is applied to get an extension of the Bauer-Fike inequality on condition numbers of similarities that block diagonalized matrices.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9411.html} }
TY - JOUR T1 - Extensions of the Kantorovich Inequality and the Bauer-Fike Inequality AU - Sun , Ji-Guang JO - Journal of Computational Mathematics VL - 4 SP - 360 EP - 368 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9411.html KW - AB -

This paper proves a Kantorovich-type inequality on the matrix of the type $\frac{1}{2}(Q^H_1 AQ_1 Q^H_1A^{-1} Q_1+Q^H_1A^{-1}Q_1Q^H_1AQ_1)$, where $A$ is an $n\times n$ positive definite Hermitian matrix and $Q_1$ is an $n\times m$ matrix with rank $(Q_1)=m$. The result is applied to get an extension of the Bauer-Fike inequality on condition numbers of similarities that block diagonalized matrices.

Sun , Ji-Guang. (1991). Extensions of the Kantorovich Inequality and the Bauer-Fike Inequality. Journal of Computational Mathematics. 9 (4). 360-368. doi:
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