Innovation based on Gaussian elimination to compute generalized inverse AT,S(2)

In this paper, we execute elementary row and column operations on the partitioned matrix (GAGGG0) into ((Is000)00−AT,S(2))to compute generalized inverse AT,S(2) of a given complex matrix AA, where GG is a matrix such that R(G)=TR(G)=T and N(G)=SN(G)=S. The total number of multiplications and divisions operations is T(m,n,s)=2mn2+4m−s−12ns+(m−s)ns+mns and the upper bound of T(m,n,s)T(m,n,s) is less than 6mn2−32n3−12n2 when n≤mn≤m. A numerical example is shown to illustrate that this method is correct.