87
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Multiplicative perturbation bounds for the block Cholesky downdating problem

&
Pages 2421-2435 | Received 24 Apr 2019, Accepted 15 Nov 2019, Published online: 08 Dec 2019
 

ABSTRACT

In this paper, we give the explicit expressions for the strong and the weak rigorous multiplicative perturbation bounds for the block Cholesky downdating problem. First, we derived the strong rigorous multiplicative perturbation bounds by combining the modified matrix-vector equation approach with the strategy for Lyapunov majorant function and the Banach fixed point theorem. Then, the weak rigorous multiplicative bounds are obtained with the help of the matrix-equation approach. The obtained results are illustrated by numerical tests.

AMS SUBJECT CLASSIFICATIONS:

Acknowledgments

The authors appreciate the constructive remarks and suggestions of the anonymous referees that helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by the National Natural Science Foundation of China (Grant Nos. 11671060, 11571062, and 11771062).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.