  Linear polymers adsorbing on a wall can be modelled by half-space
self-avoiding walks adsorbing on a line in the square lattice, or on a surface
in the cubic lattice. In this paper a numerical approach based on the GAS
algorithm is used to approximately enumerate states in the partition function
of this model. The data are used to approximate the free energy in the model,
from which estimates of the location of the critical point and crossover
exponents are made. The critical point is found to be located at
\begin{equation} a_c^+ = \cases{ 1.779 \pm 0.003, & \hbox{in the square
lattice}; \\ 1.306 \pm 0.007, & \hbox{in the cubic lattice}. } \end{equation}
These results are then used to estimate the crossover exponent $\phi$
associated with the adsorption transition, giving \begin{equation} \phi =
\cases{ 0.496 \pm 0.009, & \hbox{in two dimensions}; \\ 0.505 \pm 0.006, &
\hbox{in three dimensions}. } \end{equation} In addition, the scaling of these
thermodynamic quantities is examined using the numerical data, including the
scaling of metric quantities, and the partition and generating functions. In
all cases results and numerical values of exponents were obtained which are
consistent with estimates in the literature.
