The residual and the error for collocation methods (Q5945175)

The paper concerns the analysis of collocation methods for the solution of ordinary differential equations using operator methods. The results are based on the fact that the norms of certain collocation matrices related to the solution and its derivatives and the norms of the corresponding inverse operators are asymptotically the same. The behaviour of similar matrices related to the residual is studied. Moreover the use of the form of the residual instead of its norm in measuring the error is justified.