Preconditioning |

First, we change variables from to . Clearly, starts from , and . Then, our regression pair becomes:

This result differs from the original regression in only two minor ways, (1) revised data, and (2) a little more general form of the regularization, the extra term .

Now, let us introduce preconditioning. From the regularization, we see preconditioning introduces the preconditioning variable . Our regression pair becomes:

Here is the problem: We now require both and operators. In 2- and 3-dimensional spaces, we do not know very many operators with an easy inverse. That reason is why I found myself pushed to come up with the helix methodology of Chapter --because it provides invertible operators for smoothing and roughening.

Preconditioning |

2015-05-07