广义逆A_T^((2)),S的扰动理论(英文)

Perturbation Theory for the Generalized Inverse A_T^((2)),S

建立了广义逆A(2 )T ,S的扰动理论 .这个理论是建立在一个有用分解式的基础之上 .当 (W )条件成立且‖B -A‖很小时 ,对任意的乘法矩阵范数 ,给出了‖B(2 )T ,S-A(2 )T ,S‖的估计 .在类似的条件下 ,也给出了一般的约束线性方程组 :Ax =b ,x∈T(其中b∈AT ,dimT =dimAT)唯一解的扰动界 ,推广了相应的结论 .

A perturbation theory for the generalized inverse A (2) T,S is developed. The theory is based on a useful decomposition of B (2) T,S -A (2) T,S under( W ) condition. Norm estimate of ‖ B (2) T,S -A (2) T,S ‖ are derived for every multiplicative norm when ( W ) condition is satisfied and ‖ B-A ‖ is small. Under similiar conditions the perturbation bound for the unique solution of the general restricted system Ax=b(x∈T, b∈AT and dim( T )=dim( AT )) is studied.