發(fā)布時間：2018-10-29 08:42

【摘要】：矩陣廣義逆在線性方程組的求解,優(yōu)化問題等方面有著廣泛的應(yīng)用,矩陣的乘法擾動在最小二乘解的求解問題,分塊矩陣的廣義逆的表示等方面有著重要的意義.矩陣乘法擾動的廣義逆有不少相關(guān)的應(yīng)用,它的研究吸引了許多數(shù)學(xué)工作者的興趣.形如B =D1*AD2這種矩陣的乘積稱為矩陣4 ∈ Cm×n的一個乘法擾動,其中A是給定的,而D1∈Cm×m和D2 ∈ Cn×n可以變動,并且D1和D2兩者同時為可逆矩陣.記作矩陣A和B的Moore-Penrose逆分別為A(?)和B(?),研究A(?)和B(?)兩者之間的關(guān)系是一個具有現(xiàn)實意義的課題.本文研究的是矩陣乘法擾動的Moore-Penr ose逆的Frobenius范數(shù)估計和2-范數(shù)估計.已有不少的研究者采用奇異值分解的方法給出了‖B(?)-A(?)‖F(xiàn)和‖B(?)-A(?)‖2的上界估計,本文目的是用新的辦法改進(jìn)已有的相關(guān)結(jié)果.我們將B(?)-A(?)的表達(dá)式分為三部分之和,即:B(?)-A(?)=B(?)AA(?)-B(?)BA(?)+B(?)(Im-AA(?))-(In-B(?)B)A(?),顯然dim(BB(?))=dim(AA(?)),我們對每一部分分別進(jìn)行范數(shù)估計,通過引入?yún)��?shù)以及投影分解等辦法給出了‖B(?)-A(?)‖F(xiàn)和‖B(?)-A(?)‖2更為精細(xì)的上界估計.
[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，

本文編號：2297201