Two inverse-of-N-free methods for AM,Nâ€

We develop a new representation for the weighted Moore-Penrose inverse AM,N† of a matrix A. From this novel expression, we develop a Gauss-Jordan elimination method and a QR-based method for the computation of AM,N†. One major feature of our methods is that they do not need to compute the inverse of N. Thus, the new methods are less sensitive than the traditional Q-method on the conditioning of N. The former is suitable for computing the generalized inverses of matrices of low order “by hand” and the latter is efficient and robust for matrices of high order. Preliminary numerical testing indicates that the QR-based method is faster than the Matlab's pinv function for A†.