Symbolic and recursive computation of different types of generalized inverses

Abstract

We propose a method and algorithm for recursive computation of different classes of generalized inverses of a given one-variable rational matrix and corresponding algorithm for polynomial matrix. These methods and algorithms are generalizations of the method for computing the generalized inverses for constant matrices, originated in [F.E. Udwadia, R.E. Kalaba, A unified approach for the recursive determination of generalized inverses, Comp. Math. Appl., 37 (1999), 125–130], and the partitioning method for computing the generalized inverses of rational and polynomial matrices introduced in [P.S. Stanimirović, M.B. Tasić, Partitioning method for rational and polynomial matrices, Appl. Math. Comput., 155 (2004) 137–163; M.B. Tasić, P.S. Stanimirović, M.D. Petković, Symbolic computation of weighted Moore–Penrose inverse using partitioning method, Appl. Math. Comput 189 (2007) 615–640]. Algorithms are implemented in the symbolic computational package MATHEMATICA.