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

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,...

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Bibliographic Details
Main Authors: Belkacem Bekhiti, George F. Fragulis, George S. Maraslidis, Kamel Hariche, Karim Cherifi
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/13/2101
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Summary: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.
ISSN:2227-7390