  In many mathematical models of physical phenomenons and engineering fields,
such as electrical circuits or mechanical multibody systems, which generate the
differential algebraic equations (DAEs) systems naturally. In general, the
feature of DAEs is a sparse large scale system of fully nonlinear and high
index. To make use of its sparsity, this paper provides a simple and efficient
algorithm for computing the large scale DAEs system. We exploit the shortest
augmenting path algorithm for finding maximum value transversal (MVT) as well
as block triangular forms (BTF). We also present the extended signature matrix
method with the block fixed point iteration and its complexity results.
Furthermore, a range of nontrivial problems are demonstrated by our algorithm.
