  In this note we discuss several questions concerning the implementation of
overdetermined least-squares collocation methods for higher-index differential
algebraic equations (DAEs). Since higher-index DAEs lead to ill-posed problems
in natural settings, the dicrete counterparts are expected to be very
sensitive, what attaches particular importance to their implementation. We
provide a robust selection of basis functions and collocation points to design
the discrete problem and substantiate a procedure for its numerical solution.
Additionally, a number of new error estimates are proven that support some of
the design decisions.
