矩阵乘法扰动的Moore-Penrose逆的范数估计

发布时间：2018-10-29 08:42

【摘要】：矩阵广义逆在线性方程组的求解,优化问题等方面有着广泛的应用,矩阵的乘法扰动在最小二乘解的求解问题,分块矩阵的广义逆的表示等方面有着重要的意义.矩阵乘法扰动的广义逆有不少相关的应用,它的研究吸引了许多数学工作者的兴趣.形如B =D1*AD2这种矩阵的乘积称为矩阵4 ∈ Cm×n的一个乘法扰动,其中A是给定的,而D1∈Cm×m和D2 ∈ Cn×n可以变动,并且D1和D2两者同时为可逆矩阵.记作矩阵A和B的Moore-Penrose逆分别为A(?)和B(?),研究A(?)和B(?)两者之间的关系是一个具有现实意义的课题.本文研究的是矩阵乘法扰动的Moore-Penr ose逆的Frobenius范数估计和2-范数估计.已有不少的研究者采用奇异值分解的方法给出了‖B(?)-A(?)‖F和‖B(?)-A(?)‖2的上界估计,本文目的是用新的办法改进已有的相关结果.我们将B(?)-A(?)的表达式分为三部分之和,即:B(?)-A(?)=B(?)AA(?)-B(?)BA(?)+B(?)(Im-AA(?))-(In-B(?)B)A(?),显然dim(BB(?))=dim(AA(?)),我们对每一部分分别进行范数估计,通过引入参数以及投影分解等办法给出了‖B(?)-A(?)‖F和‖B(?)-A(?)‖2更为精细的上界估计.
[Abstract]:Matrix generalized inverse is widely used in solving linear equations and optimization problems. The multiplicative perturbation of matrix is of great significance in solving the problem of least square solution and the representation of generalized inverse of partitioned matrix. The generalized inverse of matrix multiplication perturbation has many related applications, and its research has attracted the interest of many mathematics workers. The product of a matrix such as B = D1*AD2 is called a multiplicative perturbation of the matrix 4 鈭，

本文编号：2297201