Value function iterations with transition matrix

We consider the same case as in 0919 and 0920 with transition matrix

where

but we implement the method of error bounds.

Recall that the error bounds are calculated by

where

In this model with transition matrix, we apply the same thing for all dimensions

at the same time.

If we apply it dimension by dimension(vector by vector), we fail to get the convergence.

We have to find maximum and minimum of all the changes in value functions across

States. Then we can reduce the number of iterations to get convergence.