Beyond curse of dimensionality

We implement column-by-column calculation:

from j=1 to n

to one of the following:

0: no

1:error bounds

2:policy iterations

3:policy iterations with error bounds

4:modified policy iterations

5:modified policy iterations with error bounds

And then we smooth out the points on the grid by one of the following ways:

0:linear interpolation

1:polynomial

2:LOESS

3:LOWESS

4:Kernel regression

5:Smoothing natural spline

6:NURBS

7:Bezier Curve

where we apply one of them above locally for small number of points around the

current point.

We use local index number indn around the evaluated point ks[t-1] and estimate

y=ks[t] for this x=ks[t-1] given data of k=k[indn] and k1=k[ind[indn]].

We can get almost perfect result by combining the two.

Notice that we have to use smaller order of polynomials or larger bandwidth for local

interpolation. The first or second order is usually enough.