Year 2022,
, 1550 - 1562, 01.12.2022
Mustafa Bahşi
,
Efruz Özlem Mersin
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,
, 1550 - 1562, 01.12.2022
Mustafa Bahşi
,
Efruz Özlem Mersin
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.
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.