Estimates for the inverse elements of tridiagonal matrices

In this work, new upper and lower bounds for the inverse entries of the tridiagonal matrices are presented. The bounds improve the bounds in D. Kershaw [Inequalities on the elements of the inverse of a certain tridiagonal matrix, Math. Comput. 24 (1970) 155–158], P.N. Shivakumar, C.X. Ji [Upper and lower bounds for inverse elements of finite and infinite tridiagonal matrices, Linear Algebr. Appl. 247 (1996) 297–316], R. Nabben [Two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Linear Algebr. Appl. 287 (1999) 289–305] and R. Peluso, T. Politi [Some improvements for two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Linear. Algebr. Appl. 330 (2001) 1–14].