广义逆A_(T,S)^(2)的表示与计算

Representation and Computation of Generalized Inverse A_(T,S)^(2)

比较系统的总结了AT,S(2)的各种表示,与此同时,给出AT,S(2)的三个新的表达式,AT,S(2)=[E1GA E2]-1[E10]G或AT,S(2)=G(F1 0)-1(AGF1 F2)以及AT,S(2)=-1/β0((GA)s-1+βs-1(GA)s-2+…+β2(GA)+β1In)G=-1/β0G((AG)s-1+βs-1(AG)s-2+…+β2(AG)+β1In)利用前两种表达式,我们给出AT,S(2)逆的Gauss-Jordan消去法的求法.

In this paper, we in concluded detail all kinds of representation of generalized inverse AT^（2）,S , three new expressions of which are given as following： AT^（2）,S=[E1GA E2]^-1[E1 0]G or AT^（2）,S=G（F1 0）^-1（AGF1 F2） further AT^（2）,S=-1/β0（（GA）^s-1＋βs-1（GA）^s-2＋…＋β2（GA）＋β1In）G=-1/β0G（（AG）^s-1＋βs-1（AG）^s-2＋…＋β2（AG）＋β1In）with the former two expressions, we can use Gauss-Jordan elimination to compute the generalized inverse AT^（2）,S .