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Fractional–Calculus–Based FDTD Algorithm for Ultra–Wideband Electromagnetic Pulse Propagation in Complex Layered Havriliak–Negami Media Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Avoiding Higher Matrix Powers in the Solution of Linear Dynamical Systems

Authors : Pierpaolo Natalini, Paolo Emilio Ricci

Published in: Modeling in Mathematics

Publisher: Atlantis Press

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Abstract

We show that, using Lucas polynomials of the second kind, it is possible to write down explicitly the solution of linear dynamical systems - both in the discrete and continuous case - avoiding higher matrix powers. This improves the computational complexity of the algorithms usually described in literature.

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previous chapter A Note About Generalized Forms of the Gielis Formula
next chapter On a Geometric Model of Bodies with “Complex” Configuration and Some Movements
Literature
1.
M.W.  Hirsch, S.  Smale, R.L.  Devaney, Differential equations, Dynamical Systems and An Introduction to Chaos (Academic Press, (Elsevier), San Diego - London, 2003)
2.
E.R. Scheinerman, Invitation to Dynamical Systems (Dover, New York, 2012)MATH
3.
É. Lucas, Théorie des Nombres (Gauthier-Villars, Paris, 1891)MATH
4.
I.V.V. Raghavacharyulu, A.R. Tekumalla, Solution of the Difference Equations of Generalized Lucas Polynomials. J. Math. Phys. 13, 321–324 (1972)MathSciNetCrossRefMATH
5.
M. Bruschi, P.E. Ricci, An explicit formula for \(f({\cal{A}})\) and the generating function of the generalized Lucas polynomials. Siam J. Math. Anal. 13, 162–165 (1982)MathSciNetCrossRefMATH
6.
M.  Bruschi, P.E.  Ricci, I polinomi di Lucas e di Tchebycheff in più variabili, Rend. Mat., S. VI, 13, (1980), 507–530
7.
P.E.  Ricci, Sulle potenze di una matrice, Rend. Mat. (6) 9 (1976), 179–194
8.
F.R. Gantmacher, Matrix Theory (Chelsea Pub. Co, New York, 1960)
9.
R. Lidl, C. Wells, Chebyshev polynomials in several variables. J. Reine Angew. Math. 255, 104–111 (1972)MathSciNetMATH
10.
R. Lidl, Tschebyscheff polynome in mehreren variabelen. J. Reine Angew. Math. 273, 178–198 (1975)MathSciNetMATH
11.
T.H.  Koornwinder, Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators, I–II. Kon. Ned. Akad. Wet. Ser. A, 77, 46–66 (1974)
12.
T.H. Koornwinder, Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators, III-IV. Indag. Math. 36, 357–381 (1974)MathSciNetCrossRefMATH
13.
14.
R.J. Beerends, Chebyshev polynomials in several variables and the radial part of the Laplace-Beltrami operator. Trans. Am. Math. Soc. 328(2), 779–814 (1991)MathSciNetCrossRefMATH
Metadata
Title
Avoiding Higher Matrix Powers in the Solution of Linear Dynamical Systems
Authors
Pierpaolo Natalini
Paolo Emilio Ricci
Copyright Year
2017
Publisher
Atlantis Press
Book
Modeling in Mathematics

Print ISBN: 978-94-6239-260-1

Electronic ISBN: 978-94-6239-261-8

Copyright Year: 2017

DOI
https://doi.org/10.2991/978-94-6239-261-8_9

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