Beyond curse of dimensionality

Today we use non-aggregate model and add technology change and make it fluctuate

according to some random process. We approximate the continuous random model:

by switching model with infinite many states in order:

.

.

.

where

.

.

.

for many states.

We calculate each policy function for each as it is set like:

independently for each i and calculate the next index number.

The random process can be

for as in 0818.

We implement column-by-column calculation:

from j=1 to n

when we calculate each index vector. We then smooth out the points on the gird by one

of the following:

0:linear interpolation

1:polynomial

2:LOESS

3:LOWESS

4:Kernel regression

5:Smoothing natural spline

6:NURBS

7:Bezier Curve

locally by index numbers around the evaluated points only.

We set k[ind[indn]] and k[indn] rather than k1=k[ind] and k.

We can save memory and increase n beyond curse of dimensionality.