In this article, first we will present the new rigorous perturbation bounds with normwise perturbation for the generalized Cholesky block downdating problem by combining the unified matrix–vector equation approach with the method of Lyapunov majorant functions and the Banach fixed point theorem. Then, we will derive the explicit expressions for the six distinct kinds of condition numbers, i.e. four normwise ones, mixed and componentwise ones. Furthermore, with the help of probabilistic spectral norm estimator and the small-sample statistical condition estimation method, these condition numbers can be estimated with high accuracy. At the end, the obtained results are illuminated by the numerical examples.

在本文中，首先我们将通过将统一矩阵-向量方程方法与李雅普诺夫主要函数方法和巴拿赫不动点定理相结合，为广义 Cholesky 块更新问题提出新的具有范数扰动的严格扰动界限。然后，我们将推导出六种不同的条件数的显式表达式，即四种范数，混合和分量。此外，在概率谱范数估计器和小样本统计条件估计方法的帮助下，可以高精度地估计这些条件数。最后，通过数值例子对所得结果进行了说明。