  In this paper we propose an improved fast iterative method to solve the
Eikonal equation, which can be implemented in parallel. We improve the fast
iterative method for Eikonal equation in two novel ways, in the value update
and in the error correction. The new value update is very similar to the fast
iterative method in that we selectively update the points, chosen by a
convergence measure, in the active list. However, in order to reduce running
time, the improved algorithm does not run a convergence check of the
neighboring points of the narrow band as the fast iterative method usually
does. The additional error correction step is to correct the errors that the
previous value update step may cause. The error correction step consists of
finding and recalculating the point values in a separate remedy list which is
quite easy to implement on a GPU. In contrast to the fast marching method and
the fast sweeping method for the Eikonal equation, our improved method does not
need to compute the solution with any special ordering in neither the remedy
list nor the active list. Therefore, our algorithm can be implemented in
parallel. In our experiments, we implemente our new algorithm in parallel on a
GPU and compare the elapsed time with other current algorithms. The improved
fast iterative method runs faster than the other algorithms in most cases
through our numercal studies.
