Boundary conditions and conditioning in the solution of discrete BVPs

AbstractIn this paper we study the conditioning of some discrete boundary value problems with respect to initial and terminal conditions. It is well-known that the solution of several recurrence equations is an unstable problem when its solution is found in a direct way, while when we impose initial and terminal conditions, we can approximate subdominant subspaces of the solutions. In this paper, we wish to investigate the appropriate way to impose boundary conditions in such kinds of problems. We have to point out that this study is strictly related to the study of the conditioning of band linear systems of algebraic equations