Beyond curse of dimensionality with transition matrix

After calculating the following values:

from j=1 to n

where is one of the column vectors calculated by (P*v’)’ for each dimension, we can

implement speed-up algorithms in the same way as before.

opt=0 nothing added

opt=1 error bounds

opt=2 policy iterations by direct inversion

opt=3 error bounds and policy iteration

opt=4 modified policy iteration

opt=5 error bounds and modified policy iteration

We also implement collocation method but it takes up lots of memory.

We have to keep (dim x n) x sorder in addition. When sorder is high such as sorder=9,

We can only some hundreds of n in GAUSS Light.

We then generate state numbers from transition matrix as sind from 1 to dim.

We finally simulate the movement of capital on the grid by updating:

ind[t+1]=indM[ind[t],sind[t+1]];

and

ks[t+1]=k[ind[t+1]];

starting from ks[startn] where ind[1]=startn.