  We study the principal component analysis based approach introduced by
Reisinger & Wittum (2007) and the comonotonic approach considered by Hanbali &
Linders (2019) for the approximation of American basket option values via
multidimensional partial differential complementarity problems (PDCPs). Both
approximation approaches require the solution of just a limited number of
low-dimensional PDCPs. It is demonstrated by ample numerical experiments that
they define approximations that lie close to each other. Next, an efficient
discretisation of the pertinent PDCPs is presented that leads to a favourable
convergence behaviour.
