TY - JOUR
T1 - Sensitivity analysis for the generalized Cholesky factorization
AU - Samar, Mahvish
AU - Farooq, A.
AU - Li, H.
AU - Mu, Chunlai
N1 - Generated from Scopus record by KAUST IRTS on 2023-09-21
PY - 2019/12/1
Y1 - 2019/12/1
N2 - The explicit expressions of the normwise, mixed, and componentwise condition numbers and their upper bounds for the generalized Cholesky factorization are first obtained. Then, some improved rigorous perturbation bounds with normwise or componentwise perturbation in the given matrix are derived by bringing together the modified matrix-vector equation approach with the method of Lyapunov majorant function and the Banach fixed point theorem. Theoretical and experimental results show that these new bounds are always tighter than the corresponding ones in the literature.
AB - The explicit expressions of the normwise, mixed, and componentwise condition numbers and their upper bounds for the generalized Cholesky factorization are first obtained. Then, some improved rigorous perturbation bounds with normwise or componentwise perturbation in the given matrix are derived by bringing together the modified matrix-vector equation approach with the method of Lyapunov majorant function and the Banach fixed point theorem. Theoretical and experimental results show that these new bounds are always tighter than the corresponding ones in the literature.
UR - https://linkinghub.elsevier.com/retrieve/pii/S0096300319305399
UR - http://www.scopus.com/inward/record.url?scp=85068487486&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2019.124556
DO - 10.1016/j.amc.2019.124556
M3 - Article
SN - 0096-3003
VL - 362
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -