TY - JOUR

T1 - Sensitivity analysis for the generalized Cholesky block downdating problem

AU - Farooq, Aamir

AU - Samar, Mahvish

N1 - Generated from Scopus record by KAUST IRTS on 2023-09-21

PY - 2022/1/1

Y1 - 2022/1/1

N2 - In this article, first we will present the new rigorous perturbation bounds with normwise perturbation for the generalized Cholesky block downdating problem by combining the unified matrix–vector equation approach with the method of Lyapunov majorant functions and the Banach fixed point theorem. Then, we will derive the explicit expressions for the six distinct kinds of condition numbers, i.e. four normwise ones, mixed and componentwise ones. Furthermore, with the help of probabilistic spectral norm estimator and the small-sample statistical condition estimation method, these condition numbers can be estimated with high accuracy. At the end, the obtained results are illuminated by the numerical examples.

AB - In this article, first we will present the new rigorous perturbation bounds with normwise perturbation for the generalized Cholesky block downdating problem by combining the unified matrix–vector equation approach with the method of Lyapunov majorant functions and the Banach fixed point theorem. Then, we will derive the explicit expressions for the six distinct kinds of condition numbers, i.e. four normwise ones, mixed and componentwise ones. Furthermore, with the help of probabilistic spectral norm estimator and the small-sample statistical condition estimation method, these condition numbers can be estimated with high accuracy. At the end, the obtained results are illuminated by the numerical examples.

UR - https://www.tandfonline.com/doi/full/10.1080/03081087.2020.1751033

UR - http://www.scopus.com/inward/record.url?scp=85083574140&partnerID=8YFLogxK

U2 - 10.1080/03081087.2020.1751033

DO - 10.1080/03081087.2020.1751033

M3 - Article

SN - 1563-5139

VL - 70

SP - 997

EP - 1022

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 6

ER -