Explicit inverse of a band matrix with application to computing eigenvalues of a Sturm-Liouville system

AbstractThe inverse of a symmetric tridiagonal matrix with variable entries is obtained in explicit form. It is shown how this knowledge can be applied in proving convergence of a classical finite difference method for computing eigenvalues of two-point boundary-value problems associated with the general regular Sturm-Liouville differential equation of the form (py′)′+ (λq−r)y = 0