** Next:** Diagonal weighting functions for
** Up:** Introduction
** Previous:** Introduction

In Chapter , I discussed how spectral factorization
amounts to the problem of finding an invertible square root of an
autocorrelation function.
The problem of finding an appropriate preconditioning operator for a
linear inverse problem can be considered a generalization of this.
In general, any Hessian operator can be described
as a non-stationary autocorrelation filter.
If we could find a pair of invertible non-stationary factors, they
would be the perfect preconditioning operators.
Unfortunately for large problems, however, we cannot actually form the
Hessian matrix explicitly, let alone factor it directly.

** Next:** Diagonal weighting functions for
** Up:** Introduction
** Previous:** Introduction
Stanford Exploration Project

5/27/2001