We'll also come to understand why the gradient is such a poor direction
both for steepest descent and for conjugate gradients.
An indication of our path is found in the contrast between
and exact solution
and the
gradient
(which is the first step starting from ).
Notice that differs from by the factor .This factor is sometimes called a spectrum
and in some situations it literally is a frequency spectrum.
In these cases, simply gets a different
spectrum from and many iterations are required to fix it.
Here we'll find that for many problems,
``preconditioning'' with the helix is a better way.

- PRECONDITIONED DATA FITTING
- PRECONDITIONING THE REGULARIZATION
- OPPORTUNITIES FOR SMART DIRECTIONS
- NULL SPACE AND INTERVAL VELOCITY
- INVERSE LINEAR INTERPOLATION
- EMPTY BINS AND PRECONDITIONING
- THEORY OF UNDERDETERMINED LEAST-SQUARES
- SCALING THE ADJOINT
- A FORMAL DEFINITION FOR ADJOINTS

4/27/2004