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半正定极因子在酉不变范数下的绝对与相对扰动界

THE ABSOLUTE AND RELATIVE PERTURBATION BOUNDS FOR THE HERMITIAN POSITIVE SEMIDEFINITE POLAR FACTOR UNDER UNITARILY INVARIANT NORM
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摘要 设A=QH是矩阵ACm×n的极分解,其中Q*Q=I,I为n阶单位矩阵,H为n阶Hermite半正定矩阵.给出了任意扰动下Hermite半正定极因子在酉不变范数下的绝对与相对扰动界.对于满秩矩阵,绝对与相对扰动界具有最优性质. Let A=QH be the polar decomposition of ACm×n,where Q*Q=I,the n×n identity,and H is Hermitian positive semidefinite.The absolute and relative perturbation bounds of Hermitian positive semidefinite polar factor for the matrices with different ranks are presented under any unitarily invariant norm.The absolute and relative bounds for matrices with full ranks are optimal.
作者 陈小山
出处 《华南师范大学学报(自然科学版)》 CAS 北大核心 2010年第3期1-3,共3页 Journal of South China Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(10971075) 广东省自然科学基金资助项目(91510631000021)
关键词 极分解 酉不变范数 绝对与相对扰动界 the polar decomposition unitarily invariant norm absolute and relative perturbation bounds
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