Taher, R. Ben; Mouline, M.; Rachidi, Mustapha Fibonacci-Horner decomposition of the matrix exponential and the fundamental system of solutions. (English) Zbl 1108.65073 Electron. J. Linear Algebra 15, 178-190 (2006). Using a standard computation, the authors obtain the basic Fibonacci-Horner basis, as well as the relationship between the matrix exponential and the system of fundamental solutions of an associated scalar linear differential equation of order \(r\). The problem is to compute explicitly the dynamical solution and the fundamental system of solutions of this dynamical equation. The decomposition of \(e^{tA}\) in some important situations is also studied. Some examples are discussed. Reviewer: Laura-Iulia Aniţa (Iaşi) Cited in 7 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A30 Linear ordinary differential equations and systems Keywords:matrix powers; dynamical solution; generalized Fibonacci sequence; matrix functions; numerical examples PDFBibTeX XMLCite \textit{R. B. Taher} et al., Electron. J. Linear Algebra 15, 178--190 (2006; Zbl 1108.65073) Full Text: DOI EuDML Link Link