An important component of any initial-value solver for higher-index
differential-algebraic equations consists in the computation of
consistent initial values. Estévez Schwarz and Lamour proposed an
algorithm based on projection techniques which is applicable to very
general index-2 systems. Unfortunately, the computational expense is
rather high. By exploiting certain structural assumptions tailored to
the intended application within the method of lines, we are able to
construct an implementation capable of handling systems of moderate
dimension (several thousands of unknowns). In the case of Hessenberg
systems, even optimal (i.e. linear) computational complexity is
obtained.