  We introduce a performance-optimized method to simulate localization problems
on bipartite tight-binding lattices. It combines an exact renormalization group
step to reduce the sparseness of the original problem with the recursive
Green's function method. We apply this framework to investigate the critical
behavior of the integer quantum Hall transition of a tight-binding Hamiltonian
defined on a simple square lattice. In addition, we employ an improved scaling
analysis that includes two irrelevant exponents to characterize the shift of
the critical energy as well as the corrections to the dimensionless Lyapunov
exponent. We compare our findings with the results of a conventional
implementation of the recursive Green's function method, and we put them into
broader perspective in view of recent development in this field.
