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Year 2022, Volume: 51 Issue: 6, 1550 - 1562, 01.12.2022

Mustafa Bahşi Efruz Özlem Mersin

https://doi.org/10.15672/hujms.1092305
Cited By: 1

Abstract

Keywords

Horadam numbers hyperbolic matrix functions

References

  • [1] A.H. Al-Mohy and N.J. Higham, A New Scaling and Squaring Algorithm for the Matrix Exponential, SIAM J. Matrix Anal. Appl. 31 (3), 970-989, 2009.
  • [2] M. Bahşi and S. Solak, On the Hyperbolic Fibonacci Matrix Functions, TWMS J. App. Eng. Math. 8 (2), 454-465, 2018.
  • [3] M. Bahşi and S. Solak, Hyperbolic Horadam functions, Gazi Univ. J. Sci 32 (3), 956-965, 2019.
  • [4] V.W. De Spinadel, From the Golden Mean to Chaos, Nueva Libreria, 1998, second edition, Nobuko, 2004.
  • [5] E. Defez, J. Sastre, J.J. Ibanez, and P.A. Ruiz, Matrix Functions Solving Coupled Differential Models, Math. Comput. Model. 50 (5,6), 831-839, 2009.
  • [6] E. Defez, J. Sastre, J.J. Ibanez, and P.A. Ruiz, Computing Matrix Functions Arising in Engineering Models with Orthogonal Matrix Polynomials, Math. Comput. Model. 57 (7,8), 1738-1743, 2013.
  • [7] E. Defez, J. Sastre, J.J. Ibáñez and J. Peinado, Solving engineering models using hyperbolic matrix functions, Appl. Math. Model. 40 (4), 2837-2844, 2016.
  • [8] G.I. Hargreaves, and N.J. Higham, Efficient Algorithms for the Matrix Cosine and Sine, Numer. Algorithms 40, 383-400, 2005.
  • [9] N.J. Higham, Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2008.
  • [10] N.J. Higham and M.I. Smith, Computing the Matrix Cosine, Numer. Algorithms 34, 13-16, 2003.
  • [11] A.F. Horadam, Basic Properties of a Certain Generalized Sequence of Numbers, Fibonacci Q. 3, 161-176, 1965.
  • [12] E.G. Koçer, N. Tuglu and A. Stakhov, Hyperbolic Functions with Second Order Recurrence Sequences, Ars Comb. 88, 65-81, 2008.
  • [13] J. Sastre, J.J. Ibáñez, E. Defez, and P. Ruiz, Accurate matrix exponential computation to solve coupled differential models in engineering, Math. Comput. Model. 54, 1835- 1840, 2011.
  • [14] J. Sastre, J.J. Ibáñez, P.A. Ruiz, and E. Defez, Efficient computation of the matrix cosine, Appl. Math. Comput. 219, 7575-7585, 2013.
  • [15] A.P. Stakhov and B. Rozin, On a new class of hyperbolic functions, Chaos, Solitons & Fractals 23 (2), 379-389, 2005.
  • [16] A.P. Stakhov and B. Rozin, The Golden Shofar, Chaos, Solitons & Fractals 26 (3), 677-684, 2005.
  • [17] A.P. Stakhov and I.S. Tkachenko, Hyperbolic Fibonacci Trigonometry, Reports of the National Academy of Sciences of Ukraine, In Russian, 208 (7), 9-14, 1993.

On the hyperbolic Horadam matrix functions

Year 2022, Volume: 51 Issue: 6, 1550 - 1562, 01.12.2022

Mustafa Bahşi Efruz Özlem Mersin

https://doi.org/10.15672/hujms.1092305
Cited By: 1

Abstract

In this study, we introduce a new class of the hyperbolic matrix functions which are called symmetrical hyperbolic Horadam sine and cosine matrix functions and we present some hyperbolic and recursive properties of these new matrix functions. In addition, we introduce quasi-sine Horadam matrix function and also define the matrix form of the metallic shofars that related to the hyperbolic Horadam sine and hyperbolic Horadam cosine matrix functions.

Keywords

Horadam numbers hyperbolic functions hyperbolic matrix function

References

  • [1] A.H. Al-Mohy and N.J. Higham, A New Scaling and Squaring Algorithm for the Matrix Exponential, SIAM J. Matrix Anal. Appl. 31 (3), 970-989, 2009.
  • [2] M. Bahşi and S. Solak, On the Hyperbolic Fibonacci Matrix Functions, TWMS J. App. Eng. Math. 8 (2), 454-465, 2018.
  • [3] M. Bahşi and S. Solak, Hyperbolic Horadam functions, Gazi Univ. J. Sci 32 (3), 956-965, 2019.
  • [4] V.W. De Spinadel, From the Golden Mean to Chaos, Nueva Libreria, 1998, second edition, Nobuko, 2004.
  • [5] E. Defez, J. Sastre, J.J. Ibanez, and P.A. Ruiz, Matrix Functions Solving Coupled Differential Models, Math. Comput. Model. 50 (5,6), 831-839, 2009.
  • [6] E. Defez, J. Sastre, J.J. Ibanez, and P.A. Ruiz, Computing Matrix Functions Arising in Engineering Models with Orthogonal Matrix Polynomials, Math. Comput. Model. 57 (7,8), 1738-1743, 2013.
  • [7] E. Defez, J. Sastre, J.J. Ibáñez and J. Peinado, Solving engineering models using hyperbolic matrix functions, Appl. Math. Model. 40 (4), 2837-2844, 2016.
  • [8] G.I. Hargreaves, and N.J. Higham, Efficient Algorithms for the Matrix Cosine and Sine, Numer. Algorithms 40, 383-400, 2005.
  • [9] N.J. Higham, Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2008.
  • [10] N.J. Higham and M.I. Smith, Computing the Matrix Cosine, Numer. Algorithms 34, 13-16, 2003.
  • [11] A.F. Horadam, Basic Properties of a Certain Generalized Sequence of Numbers, Fibonacci Q. 3, 161-176, 1965.
  • [12] E.G. Koçer, N. Tuglu and A. Stakhov, Hyperbolic Functions with Second Order Recurrence Sequences, Ars Comb. 88, 65-81, 2008.
  • [13] J. Sastre, J.J. Ibáñez, E. Defez, and P. Ruiz, Accurate matrix exponential computation to solve coupled differential models in engineering, Math. Comput. Model. 54, 1835- 1840, 2011.
  • [14] J. Sastre, J.J. Ibáñez, P.A. Ruiz, and E. Defez, Efficient computation of the matrix cosine, Appl. Math. Comput. 219, 7575-7585, 2013.
  • [15] A.P. Stakhov and B. Rozin, On a new class of hyperbolic functions, Chaos, Solitons & Fractals 23 (2), 379-389, 2005.
  • [16] A.P. Stakhov and B. Rozin, The Golden Shofar, Chaos, Solitons & Fractals 26 (3), 677-684, 2005.
  • [17] A.P. Stakhov and I.S. Tkachenko, Hyperbolic Fibonacci Trigonometry, Reports of the National Academy of Sciences of Ukraine, In Russian, 208 (7), 9-14, 1993.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Mustafa Bahşi 0000-0002-6356-6592

Efruz Özlem Mersin 0000-0001-6260-9063

Publication Date December 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 6

Cite

APA Bahşi, M., & Mersin, E. Ö. (2022). On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics, 51(6), 1550-1562. https://doi.org/10.15672/hujms.1092305
AMA Bahşi M, Mersin EÖ. On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics. December 2022;51(6):1550-1562. doi:10.15672/hujms.1092305
Chicago Bahşi, Mustafa, and Efruz Özlem Mersin. “On the Hyperbolic Horadam Matrix Functions”. Hacettepe Journal of Mathematics and Statistics 51, no. 6 (December 2022): 1550-62. https://doi.org/10.15672/hujms.1092305.
EndNote Bahşi M, Mersin EÖ (December 1, 2022) On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics 51 6 1550–1562.
IEEE M. Bahşi and E. Ö. Mersin, “On the hyperbolic Horadam matrix functions”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, pp. 1550–1562, 2022, doi: 10.15672/hujms.1092305.
ISNAD Bahşi, Mustafa - Mersin, Efruz Özlem. “On the Hyperbolic Horadam Matrix Functions”. Hacettepe Journal of Mathematics and Statistics 51/6 (December 2022), 1550-1562. https://doi.org/10.15672/hujms.1092305.
JAMA Bahşi M, Mersin EÖ. On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics. 2022;51:1550–1562.
MLA Bahşi, Mustafa and Efruz Özlem Mersin. “On the Hyperbolic Horadam Matrix Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, 2022, pp. 1550-62, doi:10.15672/hujms.1092305.
Vancouver Bahşi M, Mersin EÖ. On the hyperbolic Horadam matrix functions. Hacettepe Journal of Mathematics and Statistics. 2022;51(6):1550-62.

Cited By

Accurate Approximation of the Matrix Hyperbolic Cosine Using Bernoulli Polynomials
Mathematics
https://doi.org/10.3390/math11030520

https://dergipark.org.tr/en/pub/hujms