About the generalized LM-inverse and the weighted Moore–Penrose inverse

• Published in: Applied mathematics and computation Vol. 216; no. 1; pp. 114 - 124
• Main Authors: TASIC, Milan B, STANIMIROVIC, Predrag S, PEPIC, Selver H
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-03-2010; Elsevier
• Subjects: Algorithms; Computation; Equivalence; Exact sciences and technology; Generalized inverses; Inverse; LM-inverse; MATHEMATICA; Mathematical analysis; Mathematics; Matrices; Matrix methods; Numerical analysis; Numerical analysis. Scientific computation; Packages; Partitioning method; Rational matrices; Sciences and techniques of general use; Weighted Moore–Penrose inverse; Rational matrices; MATHEMATICA; Generalized inverses; Weighted Moore–Penrose inverse; LM-inverse; Partitioning method; Moore Penrose inverse; Algorithm; Implementation; Numerical analysis; Applied mathematics; Sequential method; Weighted Moore-Penrose inverse; Recursive method; Computing method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.01.019

The recursive method for computing the generalized
LM-inverse of a constant rectangular matrix augmented by a column vector is proposed in Udwadia and Phohomsiri (2007)
[16,17]. The corresponding algorithm for the sequential determination of the generalized
LM-inverse is established in the present paper. We prove that the introduced algorithm for computing the generalized
LM-inverse and the algorithm for the computation of the weighted Moore–Penrose inverse developed by Wang and Chen (1986) in
[23] are equivalent algorithms. Both of the algorithms are implemented in the present paper using the package
MATHEMATICA. Several rational test matrices and randomly generated constant matrices are tested and the CPU time is compared and discussed.