The inverses of block tridiagonal matrices

Firstly, the twisted block decompositions of the block tridiagonal matrices are presented. According to the special structure of the decomposition, the formulae of computing the block elements of each column of the inverse matrices are obtained. Then an algorithm of inverting the block tridiagonal matrices has been established. The explicit expressions of the block elements of the inverse matrices are also presented. At last, for the algorithm in this paper and some existed algorithms for the inverse matrices, the calculating complexity and the calculating time have been compared.