A Novel Recursive Algorithm for Inverting Matrix Polynomials via a Generalized Leverrie–Faddeev Scheme: Application to FEM Modeling of Wing Vibrations in a 4th-Generation Fighter Aircraft

Belkacem Bekhiti, George F. Fragulis (), George S. Maraslidis (), Kamel Hariche and Karim Cherifi
Additional contact information
Belkacem Bekhiti: Institute of Aeronautics and Space Studies (IASS), Aeronautical Sciences Laboratory, University of Blida, Blida 09000, Algeria
George F. Fragulis: Department of Electrical and Computer Engineering, ZEP Campus, University of Western Macedonia, Kozani, 50100 Kozani, Greece
George S. Maraslidis: Department of Electrical and Computer Engineering, ZEP Campus, University of Western Macedonia, Kozani, 50100 Kozani, Greece
Kamel Hariche: Institute of Electrical and Electronic Engineering, Boumerdes 35000, Algeria
Karim Cherifi: Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

Mathematics, 2025, vol. 13, issue 13, 1-28

Abstract: This paper introduces a novel recursive algorithm for inverting matrix polynomials, developed as a generalized extension of the classical Leverrier–Faddeev scheme. The approach is motivated by the need for scalable and efficient inversion techniques in applications such as system analysis, control, and FEM-based structural modeling, where matrix polynomials naturally arise. The proposed algorithm is fully numerical, recursive, and division free, making it suitable for large-scale computation. Validation is performed through a finite element simulation of the transverse vibration of a fighter aircraft wing. Results confirm the method’s accuracy, robustness, and computational efficiency in computing characteristic polynomials and adjugate-related forms, supporting its potential for broader application in control, structural analysis, and future extensions to structured or nonlinear matrix systems.

Keywords: lambda-matrices; resolvents; generalized Leverrier–Faddeev algorithm; matrix polynomials; recursion; finite element modeling; Su-30 wing structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/13/2101/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/13/2101/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:13:p:2101-:d:1688395

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().