Speedup algorithm: error bounds

We add the same error bounds:

where

as yesterday’s with some convergence criterion.

Convergence criterion would be

where all the elements in change of value function are less than tolerance level.

Say, tol=1e-8=0.00000001.

The convergence of value function without error bounds option

where we start from the bottom and go up to the ceiling with more than 100 iterations.

The convergence of value function with error bounds option

where less than 10 iterations lead to the convergence.

If we put leisure utility, the convergences may start from above down to the bottom

due to negativity.

In either case, the level of value functions does not mean anything because we start

from zero level for simplicity. The relative location matters for the calculation.