4 research outputs found
Computing generalized inverses using LU factorization of matrix product
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and
the Moore-Penrose inverse of a given rational matrix A is established. Classes
A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R*
and T*(AT*)+, where R and T are rational matrices with appropriate dimensions
and corresponding rank. The proposed algorithm is based on these general
representations and the Cholesky factorization of symmetric positive matrices.
The algorithm is implemented in programming languages MATHEMATICA and DELPHI,
and illustrated via examples. Numerical results of the algorithm, corresponding
to the Moore-Penrose inverse, are compared with corresponding results obtained
by several known methods for computing the Moore-Penrose inverse
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. Tasic, P.S.
Stanimirovic, M.D. Petkovic, 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. Stanimirovic, M.B. Tasic, Partitioning
method for rational and polynomial matrices, Appl. Math. Comput. 155 (2004)
137-163; M.D. Petkovic, P.S. Stanimirovic, 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
Application of block Cayley-Hamilton theorem to generalized inversion
In this paper we propose two algorithms for computation of the outer inverse with prescribed range and null space and the Drazin inverse of block matrix. The proposed algorithms are based on the extension of the Leverrier-Faddeev algorithm and the block Cayley-Hamilton theorem. These algorithms are implemented using symbolic and functional possibilities of the packages {\it Mathematica} and using numerical possibilities of {\it Matlab}