2 research outputs found
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
Computation of generalized inverses by using the LDL∗ decomposition
AbstractAn efficient algorithm, based on the LDL∗ factorization, for computing {1,2,3} and {1,2,4} inverses and the Moore–Penrose inverse of a given rational matrix A, is developed. We consider matrix products A∗A and AA∗ and corresponding LDL∗ factorizations in order to compute the generalized inverse of A. By considering the matrix products (R∗A)†R∗ and T∗(AT∗)†, where R and T are arbitrary rational matrices with appropriate dimensions and ranks, we characterize classes A{1,2,3} and A{1,2,4}. Some evaluation times for our algorithm are compared with corresponding times for several known algorithms for computing the Moore–Penrose inverse