Effective partitioning method for computing weighted Moore-Penrose inverse

We introduce a method and algorithm for computing the weighted MoorePenrose 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 [24] 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 [22] and [23] to the case of weighted MoorePenrose inverse. Algorithms are implemented in the symbolic computational package MATHEMATICA. AMS Subj. Class.: 15A09, 68Q40.