Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Computation of generalized inverses by using the LDL∗ decomposition

Ivan P Stanimirovic
Milan B. Tasic
Department: Department of Mathematics, Faculty of Science
Journal / Anthology

Applied Mathematics Letters
Year: 2012
Volume: 25
Issue: 3
Page range: 526-531

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.