一类矩阵反问题的扰动分析(英文)

PERTURBATION ANALYSIS OF A CLASS OF MATRIX INVERSE PROBLEMS

考虑一类矩阵反问题 minA∈ l A‖ A-A‖F,其中 l A={A∈Rn× m |‖ AX-B‖F=min},A∈ Rn× m ,X∈ Rm× p ,B∈Rn× p是给定的矩阵 ,讨论了当 A,X,B有扰动时问题解的稳定性 ,作出了问题解的扰动分析 ,对相容和不相容两种情况给出了解的扰动上界。所获得的扰动上界是相对于扰动解到无扰动流形的距离。

A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.