On computing of integer positive powers for one type of tridiagonal and antitridiagonal matrices of even order

Subject Areas : Linear and multilinear algebra; matrix theory

M. Beiranvand ¹ , M. Ghasemi Kamalvand ²

1 - Department of Mathematics, Lorestan University, Khorramabad, Iran
2 - Department of Mathematics, Lorestan University, Khorramabad, Iran

Received: 2021-01-27 Accepted : 2021-03-27 Published : 2021-03-01

Keywords:

References:

[1] R. P. Agarwal, Difference equations and inequalities, Marcel-Dekker, New York. 1992.

[2] M. Beiranvand, M. Ghasemi Kamalvand, Explicit expression for arbitrary positive powers of special tridiagonal matrices, J. Appl. Math. 2020, 2020:7290403.

[3] J. Gutierrez, Binomial cofficients and powers of large tridiagonal matrices with constant diagonals, Appl. Math. Comput. 219 (2013), 9219-9222.

[4] J. Gutierrez, Positive integer powers of certain tridiagonal matrices, Appl. Math. Comput. 202 (2008), 133-140.

[5] P. Horns, Ch. Johnson, Martin Analysis, Cambridge University Press, 1968.

[6] G. James, Advanced Modern Engineering Mathematics, Addisson-Wesley, 1994.

[7] G. Leonaite, J. Rimas, Analysis of multidimensional delay system with chain form structure, Proceeding of the 17th International Symposium on Mathematical Theory of Networks and systems, Kyoto, Japan, 2006.

[8] A. Oteles, M. Akbulak, Positive integer powers of certain complex tidiagonal matrices, Math. Sci. Lett. 2-1 (2013), 63-72.

[9] A. Oteles, M. Akbulak, Positive integer powers of certain complex tidiagonal matrices, Appl. Math. Comput. 219 (2013), 10488-10455.

[10] A. Oteles, M. Akbulak, Positive integer powers of one type of complex tridiagonal matrix, Bull. Malays. Math. Sci. Soc. 37 (4) (2014), 971-981.

[11] R. W. Picard, I. M. Elfadel, Structure of aura and co-occurrence matrices for the Gibbs texture model, J. Math. Imaging. Vision. 2 (1) (1992) 5-25.

[12] J. Rimas, Investigation of dynamics of mutually synchronized system, Telecocommunications. Radio. Engin. 32 (2) (1977), 68-73.

[13] J. Rimas, On Computing of arbitrary positive integer powers for one type of tridiagonal matrices of even order, Appl. Math. Comput. 164 (2005), 829-835.

[14] J. Rimas, On computing of orbitary positive integer powers for one type of tridiagonal matrices with elements 1,0,0,··· ,0,1 in principal and 1,1,1,··· ,1,1 in neighboring diagonals-I, Appl. Math. Comput. 186 (2007), 1254-1257.

[15] J. Rimas, On computing of orbitary positive integer powers for one type of tridiagonal matrices with elements 1,0,0,··· ,0,1 in principal and 1,1,1,··· ,1,1 in neighboring diagonals-II, Appl. Math. Comput. 187 (2007), 1472-1475.

[16] J. Rimas, On computing of orbitary positive integer powers for one type of symmetric tridiagonal matrices of even order, Appl. Math. Comput. 172 (2006), 245-251.

[17] S. E. Umbaugh, Computer Imaging: Digital Image Analysis and Processing, The CRC Pres, 2005.