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广义Cholesky分解和Cholesky-like分解的严格
乘法扰动界
杨艳飞，李寒宇
重庆大学数学与统计学院，重庆市 401331
摘要：广义Cholesky分解和Cholesky-like分解是经典的Cholesky分解的推广。本文结合矩阵方
程和改进的矩阵方程方法，给出了关于这两个分解的严格乘法扰动界。作为特殊情况，我们也
给出了这两个分解的相应的一阶乘法扰动界。其中的一些结果改进了现有的结果。
关键词：乘法扰动；Generalized Cholesky分解；Cholesky-like分解；严格扰动界；一阶扰动界
中图分类号： 15A23; 15A45
Rigorous multiplicative perturbation bounds for
the generalized Cholesky factorization and the
Cholesky-like factorization
YANG Yan-Fei , LI Han-Yu
Department of Mathematics and Statistics, University of Chongqing, Chongqing 401331
Abstract: The generalized Cholesky factorization and the Cholesky-like factorization are
two generalizations of the classic Cholesky factorization. In this paper, the rigorous
multiplicative perturbation bounds for the two factorizations are derived using the matrix
equation and the refined matrix equation approaches. The corresponding first order
multiplicative perturbation bounds, as special cases, are also presented. Some of these results
improve the corresponding ones given in the literature.
Key words: Multiplicative perturbation; Generalized Cholesky factorization; Cholesky-like
factorization; Rigorous perturbation bound; First order perturbation bound
0 Introduction
Let R
m×n
be the set of m × n real matrices and R
m×n
r
be the subset of R
m×n
consisting
of matrices with rank r. Let I
r
be the identity matrix of order r. For a matrix A ∈ R
m×n
,
基金项目： the National Natural Science Foundation of China (Grant No.11201507)，and the Natural Science
Foundation Project of CQ CSTC (Grant No. 2010BB9215)
作者简介： Yang yanfei（1987-），female，student，major research direction：matrix perturbation analysis theory.
Correspondence author：Li HanYu （1981-），male，associate professor，major research direction：numerical linear
algebra.
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