Effective partitioning method for computing weighted Moore–Penrose inverse

We introduce a method and an algorithm for computing the weighted Moore–Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are generalizations of algorithms developed in [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] to multiple-variable rational and polynomial matrices and improvements of these algorithms on sparse matrices. Also, these methods are generalizations of the partitioning method for computing the Moore–Penrose inverse 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.D. Petković, P.S. Stanimirović, Symbolic computation of the Moore–Penrose inverse using partitioning method, Internat. J. Comput. Math. 82 (2005) 355–367] to the case of weighted Moore–Penrose inverse. Algorithms are implemented in the symbolic computational package MATHEMATICA.