Multiplicative perturbation bounds for the Generalized block Cholesky downdating problem

The explicit expressions for the strong and the weak rigorous multiplicative perturbation bounds for the Generalized block Cholesky downdating problem are obtained. By bringing together the modified matrix-vector equation approach with the method of Lyapunov majorant function and the Banach fixed point theorem, we derived the strong rigorous multiplicative perturbation bounds. By using the matrix-equation approach the weak rigorous multiplicative bounds are presented. Numerical experiments are provided to illustrate the obtained results.