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Effective partitioning method for computing generalized inverses and their gradients

Marko D. Petkovic
Milan B. Tasic
Department: Department of Mathematics, Faculty of Science
Predrag S. Stanimirovic
Journal / Anthology

Applied Mathematics and Computation
Year: 2011
Volume: 217
Issue: 19
Page range: 7588-7598

We extend the algorithm for computing {1}, {1, 3}, {1,4} inverses and their gradients from [11] to the set of multiple-variable rational and polynomial matrices. An improvement of this extension, appropriate to sparse polynomial matrices with relatively small number of nonzero coefficient matrices as well as in the case when the nonzero coefficient matrices are sparse, is introduced. For that purpose, we exploit two effective structures form [6], which make use of only nonzero addends in polynomial matrices, and define their partial derivatives. Symbolic computational package Mathematica is used in the implementation. Several randomly generated test matrices are tested and the CPU times required by two used effective structures are compared and discussed.