Lobachevskii Journal of Mathematics

, Volume 36, Issue 1, pp 28–37 | Cite as

Explicit eigenvalues of some perturbed heptadiagonal matrices via recurrent sequences

Article

Abstract

In this paper we present a direct method to calculate explicit expressions of eigenvalues of some perturbed heptadiagonal matrices. The method is of interest to engineers and statisticians since it is based on elementary properties of determinants and recurrent sequences. The use and even the knowledge of the theory of orthogonal polynomials, which was usually necessary (see for example [2]) is not needed here. Once the needed recurent relations are obtained, we use the theory of recurrent sequences and trigonometric formulas.

Keywords and phrases

Eigenvalues heptadiagonal matrices characteristic polynomial recurrent relation 

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References

  1. 1.
    R. P. Agarwal, Difference Equations and Inequalities (Marcel Dekker, 1992).MATHGoogle Scholar
  2. 2.
    A. H. Ahmed Driss and E. Mohamed, Applied Mathematics and Computation 198(1), 634–642 (2008).MATHMathSciNetGoogle Scholar
  3. 3.
    R. Álvarez-Nodarse, J. Petronilho, and N. R. Quintero, J. Comput. Appl.Math. 184(2), 518–537 (2005).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    N. D. Cahill and D. A. Narayan, Fibonacci Quart. 42(3), 216–221 (2004).MATHMathSciNetGoogle Scholar
  5. 5.
    J. Cao and J. Sun, Int. J. for Numerical Analysis Simulation 2, 15–27.Google Scholar
  6. 6.
    D. G. Opoku, Dimitris G. Triantos, Fred Nitzsche, and Spyros G. Voutsinas, ICAS 2002 Congress, pp. 299.1–299.11 (2002).Google Scholar
  7. 7.
    M. El-Mikkawy, Applied Mathematics and Computation 139, 503–511 (2003).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Fabrício A. B. Silva, E. P. Lopes, and Eliana P. L. Aude, Flavio Mendes, Henrique Serdeira1, Julio Silveira1, Proc. of the 36th Annual Simulation Symposium (ANSS’03) (2003).Google Scholar
  9. 9.
    R. M. Gray, Foundations and Trends in Communications and Information Theory 2(3), 155–239 (2006).CrossRefGoogle Scholar
  10. 10.
    K. A. Hoffmann, and S. T. Chiang, Computational Fluid Dynamics For Engineers (Engineering Education System, Kansas, 1993), Vol. 1.Google Scholar
  11. 11.
    M. Ilicak, A. Ecder, and E. Turan, Int. J. of Computer Mathematics 84(6), 783–793 (2007).CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    E. Kilic, Applied Mathematics and Computation 204, 184–190 (2008).CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    E. Kilic and D. Tasci, J. Comput. Appl. Math. 201(1), 182–197 (2007).CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    S. Kouachi, Electronic J. of Linear Algebra 15, 115–133 (2006).MATHMathSciNetGoogle Scholar
  15. 15.
    S. Kouachi, Appl. Math. (Warsaw) 35, 107–120 (2008).CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    S. Kouachi, “Direct Methods to Calculate Explicit Eigenvalues of Pentadiagonal Matrices”, submitted to Ensaios Matematicos.Google Scholar
  17. 17.
    A. Martńez, L. Bergamaschi, M. Caliari, and M. Vianello, J. of Computational and Applied Mathematics (in press).Google Scholar
  18. 18.
    J. Rimas, Applied Mathematics and Computation 204, 120–129 (2008).CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    J. Rimas, Applied Mathematics and Computation 174, 997–1000 (2006).CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    D. K. Salkuyeh, Applied Mathematics and Computation 176, 442–444 (2006).CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    R. Wituła and D. Słota, Applied Mathematics and Computation 189(1), 514–527 (2007).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceQassim UniversityAl-Gassim, BuraydahSaudi Arabia

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