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.

翻译：获得了通用区块 Choolesky 下沉问题强大和薄弱的多倍扰动边框的清晰表达。通过将修改的矩阵-矢量方程法与 Lyapunov 多数函数和 Banach 固定点定点定律法结合起来,我们得出了强烈的多倍扰动边框。通过使用矩阵-对称法,提出了薄弱的严格倍增边框。提供了数字实验,以说明所获得的结果。