埃尔米特矩阵的矩阵函数条件数与扰动
数值分析
2012-06-20 v2
摘要
考虑定义在埃尔米特矩阵上的矩阵函数 。本文有两个目的：推导矩阵函数的绝对结构化条件数的新结果，并给出扰动 的新界，该界用 和 的特征值表示。结果具有一般性，且在特定条件下对任意酉不变矩阵范数 成立。我们通过电子结构理论计算中的误差分析应用来说明这些公式的用途。
引用
@article{arxiv.1206.1762,
title = {On the condition number and perturbation of matrix functions for Hermitian matrices},
author = {Elias Jarlebring and Emanuel H. Rubensson},
journal= {arXiv preprint arXiv:1206.1762},
year = {2012}
}
备注
Shortly after submission of this manuscript we discovered that Lemma 2 does not hold under the stated conditions. In order to have the time to carefully work out and understand the reason for this error and hopefully correct it, we have decided to withdraw the manuscript