The analytic inversion of any finite symmetric tridiagonal matrix
Hashim A. Yamani, Mohamed S. Abdelmonem · Journal of Physics A Mathematical and General · 1997
We use the theory of orthogonal polynomials to write down explicit expressions for the polynomials of the first and second kind associated with a given infinite symmetric tridagonal matrix H. The Green's function is the inverse of the infinite symmetric tridiagonal matrix (H-zI). By calculating the inverse of the finite symmetric tridiagonal matrix we can find the analytical form of the inverse of the finite symmetric tridiagonal matrix, .