Extensions of Faddeev’s algorithms to polynomial matrices

• Published in: Applied mathematics and computation Vol. 214; no. 1; pp. 246 - 258
• Main Authors: Stanimirović, Predrag S., Tasić, Milan B., Vu, Ky M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.08.2009; Elsevier
• Subjects: Drazin inverse; Exact sciences and technology; Leverrier–Faddeev algorithm; MATHEMATICA; Mathematical analysis; Mathematics; Moore–Penrose inverse; Numerical analysis; Numerical analysis. Scientific computation; Polynomial matrices; Sciences and techniques of general use; Drazin inverse; MATHEMATICA; Leverrier–Faddeev algorithm; Moore–Penrose inverse; Polynomial matrices; Polynomial; Numerical analysis; Moore Penrose inverse; Applied mathematics; Leverrier-Faddeev algorithm; Control system; Algorithm; Moore-Penrose inverse; Implementation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.03.076

Starting from algorithms introduced in [Ky M. Vu, An extension of the Faddeev’s algorithms, in: Proceedings of the IEEE Multi-conference on Systems and Control on September 3–5th, 2008, San Antonio, TX] which are applicable to one-variable regular polynomial matrices, we introduce two dual extensions of the Faddeev’s algorithm to one-variable rectangular or singular matrices. Corresponding algorithms for symbolic computing the Drazin and the Moore–Penrose inverse are introduced. These algorithms are alternative with respect to previous representations of the Moore–Penrose and the Drazin inverse of one-variable polynomial matrices based on the Leverrier–Faddeev’s algorithm. Complexity analysis is performed. Algorithms are implemented in the symbolic computational package MATHEMATICA and illustrative test examples are presented.