Computing generalized inverses using LU factorization of matrix product

Abstract

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, corres-ponding to the Moore–Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore–Penrose inverse.

Keywords:

• cholesky factorizations
• generalized inverses
• Moore–Penrose inverse
• MATHEMATICA
• DELPHI

2000 AMS Subject Classification: :

• 15A09
• 68Q40