There is a simple heuristic argument (see, for example, Press et al. [125
, Section 9.6]) that at least some spurious local
minima should be expected. We are trying to solve a system of
nonlinear equations,
(one
equation for each horizon-surface grid point). Equivalently, we are trying to find the intersection of the
codimension-one hypersurfaces
in surface-shape space. The problem is that anywhere two or more of these
hypersurfaces approach close to each other, but do not actually intersect, there is a spurious local minimum in
.