ABSTRACT 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.

中文翻译：

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块 Cholesky 降级问题的乘法扰动边界

摘要 在本文中，我们给出了块 Cholesky 降级问题的强和弱严格乘法扰动边界的显式表达式。首先，我们通过将修正矩阵向量方程方法与 Lyapunov 主函数策略和 Banach 不动点定理相结合，推导出强严格乘法扰动界。然后，借助矩阵方程方法获得弱严格乘法界。所得结果通过数值试验说明。