On the factorization and the inverse of a tridiagonal matrix

References

• A. Amiraslani, R.M. Corless and P. Lancaster, Linearization of matrix polynomials, IMA J. Num. Anal., 29 (2009), 141-157 doi: 10.1093/imanum/drm051
   Web of Science ®Google Scholar
• L. Aceto, P. Ghelardoni, C. Magherini, Boundary value methods for the reconstruction of Sturm-Liouville potentials, Appl. Math. Comput. 219 (2012)2960-2974.
   Web of Science ®Google Scholar
• D. Kaya, An explicit and numerical solutions of some fifth-order Kdv equation by decomposition method, Appl. Math. Comput. 144 (2003) 353-363.
   Web of Science ®Google Scholar
• S.M. El-Sayed, D. Kaya, An application of the ADM to seven order Sawada Kotara equations, Appl. Math. Comput. 157 (2004) 93-101.
   Web of Science ®Google Scholar
• Jie Shen, Tao Tang, Spectral and High-Order Methods with Applications, Science Press, Beijing, 2006
   Google Scholar
• J. Monterde, H. Ugail, A general 4th-order PDE method to generate bezier surfaces from the boundary, Comput. Aided Geom. Design 23 (2006) 208-225. doi: 10.1016/j.cagd.2005.09.001
   Web of Science ®Google Scholar
• P.G. Patil, Y.S. Swamy, An eficient model for vibration control by piezoelectric smart structure using finite element method, Eur. J. Comput. Sci. Netw.Secu. 8 (2008) 258-264.
   Google Scholar
• J.S. Respondek, Numerical recipes for the high efficient inverse of the confluent Vandermonde matrices, Appl. Math. Comput. 218 (2011) 2044-2054.
   Web of Science ®Google Scholar
• J.S. Respondek, Recursive numerical recipes for the high efficient inversion of the confluent Vandermonde matrices, Appl. Math. Comput. 225 (2013)718-730.
   Web of Science ®Google Scholar
• H. Li, D. Zhao, An extension of the Golden-Thompson theorem, J. Inequal.Appl. (2014).
   Web of Science ®Google Scholar
• H.Y. Li, Z.G. Gong, D. Zhao, Least squares solutions of the matrix equation AXB+CYD=E with the least norm for symmetric arrowhead matrices, Appl.Math. Comput. 226 (2014) 719-724.
   Web of Science ®Google Scholar
• Chaojie Wang, Hongyi Li, Di Zhao, An explicit formula for the inverse of a pentadiagonal Toeplitz matrix, Journal of Computational and Applied Mathematics 278 (2015) 12-18 doi: 10.1016/j.cam.2014.08.010
   Web of Science ®Google Scholar
• A. Hadj, M. Elouafi, A fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix, Appl. Math. Comput. 202 (2008) 441-445.
   Web of Science ®Google Scholar
• E.N. Antoniou and S. Vologiannidis, A new family of companion forms of polynomial matrices, ELA, 11 (2004), 78-87. doi: 10.13001/1081-3810.1124
   Google Scholar
• J.L. Aurentz, R. Vanebril and D.S. Watkins, Fast computation of eigenvalues of companion, comrade and related matrices, BIT Numer. Math., 54 (2014), 7-30. doi: 10.1007/s10543-013-0449-x
   Web of Science ®Google Scholar
• S. Barnett, Division of generalized polynomials using the comrade matrix, Linear Algebra Appl., 60 (1984), 159-175. doi: 10.1016/0024-3795(84)90077-6
   Web of Science ®Google Scholar
• Emrah Kılıç (2008). Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions. Applied Mathematics and Computation, 197(1), 345-357. doi: 10.1016/j.amc.2007.07.046
   Web of Science ®Google Scholar
• J. Abderraman Marrero and V. Tomeo, On the closed representation for the inverses of Hessenberg matrices, J. Comput. Appl. Math. 236 (2012), no. 12, 2962-2970. doi: 10.1016/j.cam.2011.07.008
   Web of Science ®Google Scholar
• J. Abderraman Marrero, V. Tomeo and E. Torrano, On inverses of infinite Hessenberg matrices, J. Comput. Appl. Math. 275 (2015), 356-365. doi: 10.1016/j.cam.2014.07.010
   Web of Science ®Google Scholar
• B. Bukhberger and G. A. Emel’ yanenko, Methods of inverting tridiagonal matrices, USSR Comput. Math. and Math. Phys. 13 (1973), no. 3, 10-20. doi: 10.1016/0041-5553(73)90096-7
   Google Scholar
• B. Talibi, A. Aiat Hadj, D. Sarsri, A numerical algorithm for computing the inverse of a Toeplitz pentadiagonal matrix, Applied Mathematics and Computational Mechanics 2018, 17(3), 83-95. doi: 10.17512/jamcm.2018.3.08
   Web of Science ®Google Scholar
• Y. Ikebe, On inverses of Hessenberg matrices, Linear Algebra Appl. 24 (1979), 93-97. doi: 10.1016/0024-3795(79)90149-6
   Web of Science ®Google Scholar
• J. Maroulas, Factorization of Hessenberg matrices, Linear Algebra Appl. 506 (2016), 226-243. doi: 10.1016/j.laa.2016.05.026
   Web of Science ®Google Scholar