In this paper, we study some structural properties of M-matrices and inverse M-matrices. Based on the UL and LU decompositions of an nonsingular tri-diagonal matrix, we get explicit formulas for calculating the entries of the inverse of tri-diagonal M-matrices, which are presented based on their sub-determinants that can be calculated in recurrence.
['Chuansheng Yang']
Some properties and computing inverses of tri-diagonal M-matrices