On inverses of tridiagonal matrices

An algorithm for computing the inverse of a general tridiagonal matrix is introduced. This algorithm is obtained by factoring this matrix into the product of two bidiagonal matrices using Crout's LU factorization, one upper and one lower bidiagonal. A simple recurrence relation is used to generate a sequence of numbers, this sequence is then used to fill in the matrices L, u, L-1, u(-1) and consequently the required inverse.