Abstract: Predrag Stanimirović

METHODS FOR COMPUTING GENERALIZED INVERSES OF MATRICES

 

Symbolic computation of generalized inverses is one of the interesting application areas of computer algebra. During the symbolic implementation, variables are stored in "exact" form or can be left "unassigned" (without numerical values) resulting in no loss of accuracy during the calculation.We extended several methods based on the Cayley-Hamiltontheorem,Grevile's partitioning method, the full-rank factorization and the LU factorization to the set of polynomial and/or rationalmatrices.Also, effective versions of these algorithms, appropriate for polynomial matrices where only a few polynomial coefficients are nonzero, are developed. The set of one-variable as well as the set of multiple-variable polynomial matrices are considered. We also developed an algorithm for rapid computation of Moore-Penrose, $\{2,3\}$ and $\{2,4\}$ generalized inverses,with complexity which is not greater than the matrix multiplication complexity. Several iterative algorithms for computing Moore-Penrose inverse are developed.

 

 

Joint work with:  Marko Petković, Milan Tasić