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Tytuł artykułu

Explicit formulas for the constituent matrices. Application to the matrix functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences. Some connections with other results are supplied. Furthermore,we manage to provide tractable expressions for the matrix functions, and for illustration purposes we establish compact formulas for both the matrix logarithm and the matrix pth root. Some examples are also provided.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2014-11-11
zaakceptowano
2015-03-12
online
2015-03-23
Twórcy
autor
  • Département de Mathématiques et Informatique, Faculté des Sciences,Université Moulay Ismail, B.P. 4010, Beni
    M’hamed, Méknés, Morocco
autor
  • Associate researcher with "Equip of DEFA", Département de Mathématiques
    et Informatique, Faculté des Sciences,Université Moulay Ismail, B.P. 4010, Beni M’hamed, Méknés, Morocco
Bibliografia
  • [1] J. Abderramán Marrero, R. Ben Taher and M. Rachidi, On explicit formulas for the principal matrix logarithm, AppliedMathematics and Computation Vol. 220 (2013), p. 142-148.[WoS]
  • [2] J. Abderramán Marrero, R. Ben Taher, Y. El Khattabi and M. Rachidi, On explicit formulas of the principal matrix p − th rootby polynomial decompositions, Applied Mathematics and Computation Vol. 242 (2014), p. 435-443.[WoS]
  • [3] R. Ben Taher and M. Rachidi, Linear matrix differential equations of higher-order and applications, Electronic Journal ofDifferential Equations Vol. 2008 No.95 (2008), p.1-12.
  • [4] R. Ben Taher and M. Rachidi, On the matrix powers and exponential by r-generalized Fibonacci sequences methods: thecompanion matrix case, Linear Algebra and Its Applications Vol. 370 (2003), p. 341-353.
  • [5] R. Ben Taher and M. Rachidi, Linear recurrence relations in the algebra matrices and applications, Linear Algebra and ItsApplications Vol. 330 (2001), p. 15-24.
  • [6] R. Ben Taher, I. Bensaoud and M. Rachidi; Dynamic solutions and computation of the powers and exponential of matrix,International Journal of Mathematics, Game Theory and Algebra Vol. 13 No. 6 (2003), p. 455-463.
  • [7] R. Ben Taher, M. Mouline and M. Rachidi, Fibonacci-Horner decomposition of the matrix exponential and the fundamentalsolution, Electronic Linear Algebra Vol. 15 (2006), p. 178-190.
  • [8] R. Ben Taher, Y. El khatabi and M. Rachidi, On the polynomial decompositions of the principal matrix p − th root andapplications, Int. Journal of Contemp. Math. Sciences, Vol. 9, No. 3 (2014), p. 141-152 .
  • [9] F-C. Chang, A Direct Approach to the Constituent Matrices of an Arbitrary Matrix with Multiple Eigenvalues, Proceedingsof the IEEE, Vol. 65 No. 10 (October 1977), p. 1509-1510.
  • [10] W. J. Culver, On the existence and uniqueness of the real logarithm of matrix, Proceeding of the American MathematicalSociety Vol. 17 No. 5 (1966), p. 1146-1151.
  • [11] F. Dubeau,W. Motta, M. Rachidi and O. Saeki, On weighted r-generalized Fibonacci sequences, Fibonacci Quarterly Vol. 35(1997), p. 102-110.
  • [12] F. R. Gantmacher, Theory of Matrices. Chelsea Publishing Company, New York, 1959.
  • [13] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. Cambridge Univ. Press, Cambridge, UK, 1991.
  • [14] Sh-H. Hou and Ed. Hou, Recursive computation of inverses of confluent Vandermonde matrices, The Electronic Journal ofMathematics and Technology Vol. 1 Issue 1, ISSN 1933-2823, (2007)
  • [15] P. Lancaster and M. Tismenetsky The Theory of Matrices: With Applications. Orlando Academic Press- Computer Scienceand Applied Marthematics, 1985.
  • [16] W.G. Kelly and A.C. Peterson, Difference equations: an introduction with applications, Academic Press, San Diego 1991.
  • [17] M. Mouline and M. Rachidi, Application of Markov chains properties to r-generalized Fibonacci sequences, FibonacciQuarterly Vol. 37 (1999), p. 34-38.
  • [18] R. F. Rinehart, The Equivalence of Definitions of a Matrice Function, The AmericanMathematicalMonthly Vol. 62 No. 6 (Jun- Jul. 1955), p. 395-414
  • [19] H.J. Runckel, U. Pittelkow. Practical computation of matrix functions. Linear Algebra Appl. Vol. 49 (1983), p. 161-178.
  • [20] R. P. Stanley, Enumerative combinatorics, Cambridge University Press, U.K. Vol. I 1997.
  • [21] A. Sadeghi, A. Izani, Md. Ismail and A. Ahmad, Computing the pth Roots of a Matrix with Repeated Eigenvalues, AppliedMathematical Sciences Vol. 5, No. 53 (2011), p. 2645-2661.
  • [22] G. Sobczyk The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly Vol. 108 No.4(Apr.,2001), p. 336-346.
  • [23] L. Verde-Star, Divided differences and linearly recursive sequences, Studies in Applied Mathematics Vol. 95, (1995), p.433-456.
  • [24] L. Verde-Star, Functions of matrices, Linear Algebra and Its Applications Vol. 406 (2005), p. 285-300.
  • [25] L. Verde-Star, Interpolation approach to the spectral resolution of square matrices, L’Enseignement Mathématique Vol. 252 (2006), p. 239-253.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0004
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