On the Computation of An

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Previous article Next article On the Computation of AnSaber N. Elaydi and William A. Harris, Jr.Saber N. Elaydi and William A. Harris, Jr.https://doi.org/10.1137/S0036144597319235PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractMethods, which are based on the Cayley--Hamilton theorem, for the computation of An for nonsingular A are presented.[1] Saber Elaydi, An introduction to difference equations, Undergraduate Texts in Mathematics, Springer‐Verlag, 1999xviii+427 1711587 CrossrefGoogle Scholar[2] Edward Fulmer, Computation of the matrix exponential, Amer. Math. 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Monthly, 73 (1966), 2–7 33:2845 CrossrefISIGoogle ScholarKeywordsCayley--Hamiltondifference equationCasorati matrix Previous article Next article FiguresRelatedReferencesCited ByDetails Hyers–Ulam stability and discrete dichotomy for difference periodic systemsBulletin des Sciences Mathématiques, Vol. 140, No. 8 | 1 Nov 2016 Cross Ref Laplace and Z transforms of linear dynamical systems and conic sectionsZeitschrift für angewandte Mathematik und Physik, Vol. 67, No. 3 | 2 May 2016 Cross Ref Hyers–Ulam stability and discrete dichotomyJournal of Mathematical Analysis and Applications, Vol. 423, No. 2 | 1 Mar 2015 Cross Ref Dynamics of a Rational System of Difference Equations in the PlaneAdvances in Difference Equations, Vol. 2011, No. 1 | 1 Jan 2011 Cross Ref Ordinary Dierential and Dierence EquationsFundamentals of Linear Systems for Physical Scientists and Engineers | 29 August 2013 Cross Ref Linear Operators and MatricesFundamentals of Linear Systems for Physical Scientists and Engineers | 29 August 2013 Cross Ref Ordinary Differential and Difference EquationsFundamentals of Linear Systems for Physical Scientists and Engineers | 1 Oct 2009 Cross Ref Integers Powers of Certain Asymmetric MatricesComputational Science – ICCS 2009 | 1 Jan 2009 Cross Ref Calculating the matrix exponential of a constant matrix on time scalesApplied Mathematics Letters, Vol. 21, No. 6 | 1 Jun 2008 Cross Ref Reducibility and Stability Results for Linear System of Difference EquationsAdvances in Difference Equations, Vol. 2008 | 1 Jan 2008 Cross Ref On linear matrix differential equationsAdvances in Applied Mathematics, Vol. 39, No. 3 | 1 Sep 2007 Cross Ref Functions of matricesLinear Algebra and its Applications, Vol. 406 | 1 Sep 2005 Cross Ref Avoiding Eigenvalues in Computing Matrix PowersThe American Mathematical Monthly, Vol. 112, No. 5 | 1 February 2018 Cross Ref Remarks on the Calculation of the Power of a MatrixJournal of Difference Equations and Applications, Vol. 10, No. 2 | 25 January 2007 Cross Ref Floquet Theory for Time Scales and Putzer Representations of Matrix LogarithmsJournal of Difference Equations and Applications, Vol. 9, No. 1 | 1 Jan 2003 Cross Ref Remarks on the Notion of Order of Difference EquationsJournal of Difference Equations and Applications, Vol. 8, No. 10 | 1 Jan 2002 Cross Ref Matrix Exponentials---Another ApproachSIAM Review, Vol. 43, No. 4 | 4 August 2006AbstractPDF (497 KB)Optimal Existence Results for nth Order Periodic Boundary Value Difference EquationsJournal of Mathematical Analysis and Applications, Vol. 247, No. 1 | 1 Jul 2000 Cross Ref Existence and approximation of solutions for first-order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutionsComputers & Mathematics with Applications, Vol. 39, No. 1-2 | 1 Jan 2000 Cross Ref Volume 40, Issue 4| 1998SIAM Review765-1024 History Published online:02 August 2006 InformationCopyright © 1998 Society for Industrial and Applied MathematicsKeywordsCayley--Hamiltondifference equationCasorati matrixMSC codes15-0115A2139-0139A10PDF Download Article & Publication DataArticle DOI:10.1137/S0036144597319235Article page range:pp. 965-971ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics