Residue Arithmetic Algorithms for Exact Computation of g-Inverses of Matrices

Residue arithmetic algorithms are described for exact computation of the Moore–Penrose inverse of a rectangular matrix with rational elements.The first algorithm is based on reducing the matrix to Hermite canonical form; the second algorithm uses a partitioning procedure, while the third uses the orthgonalization procedure. A comparison of the estimates for the choice of prime moduli in different algorithms is given.