广义Cholesky分解新的扰动分析

New Perturbation Analysis for the Generalized Cholesky Factorization

设实对称矩阵K具有广义Cholesky分解,证得扰动矩阵的广义Cholesky分解满足:‖△L‖F/‖L‖2≤Kc(k)ε+O(ε2).例子表明此扰动结果比以往的结果更精确.

Suppose real symmetric matrix has the generalized Cholesky factorization,it is proved that the generalized Cholesky factorization of perturbing matrix satisfies：｜｜ΔL｜｜F/｜｜L｜｜2≤Kc（k）ε＋O（ε^2）. One example shows that this perturbation result is more precise than ever.