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On the Computation of An

1998; Society for Industrial and Applied Mathematics; Volume: 40; Issue: 4 Linguagem: Inglês

10.1137/s0036144597319235

1095-7200

Saber Elaydi, William A. Harris,

Matrix Theory and Algorithms

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. Monthly, 82 (1975), 156–159 50:13687 CrossrefISIGoogle Scholar[3] Morris Hirsch and , Stephen Smale, Differential equations, dynamical systems, and linear algebra, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York‐London, 1974xi+358, Pure and Applied Mathematics, Vol. 60 58:6484 Google Scholar[4] Po‐Fang Hsieh, , Mitsuhiko Kohno and , Yasutaka Sibuya, Construction of a fundamental matrix solution at a singular point of the first kind by means of the SN decomposition of matrices, Linear Algebra Appl., 239 (1996), 29–76 98c:65037 CrossrefISIGoogle Scholar[5] Google Scholar[6] R. B. Kirchner, An explicit formula for eAt, Amer. Math. Monthly, 74 (1967), pp. 1200–1204. aml AMMYAE Am. Math. Monthly CrossrefISIGoogle Scholar[7] J. LaSalle, Stability theory for difference equations, Math. Assoc. of America, Washington, D.C., 1977, 0–0, 1–31. Stud. in Math., Vol. 14 58:1789 Google Scholar[8] I. Leonard, The matrix exponential, SIAM Rev., 38 (1996), 507–512 10.1137/S0036144595286488 97d:34009 LinkISIGoogle Scholar[9] E. Putzer, Avoiding the Jordan canonical form in the discussion of linear systems with constant coefficients, Amer. Math. 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