Multiplicative perturbation bounds for the block Cholesky downdating problem

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.