INVERSION FORMULAS FOR TRIDIAGONAL MATRICES WITH APPLICATIONS TO BOUNDARY VALUE PROBLEMS*
Tetsuro Yamamoto · Numerical Functional Analysis and Optimization · 2001
This paper first reviews some results on the structure of inverses of nonsingular and irreducible tridiagonal matrices. Next, explicit inversion formulas are given for certain, not necessarily symmetric, tridiagonal matrices. The results are then applied to matrices arising from discretization of two-point boundary value problems of the Sturm-Liouville type. The results show harmonic relations between the Green functions and the discrete Green functions for the problems. Finally the results are extended to block tridiagonal matrices.