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Often people do calculations by the method of steepest descent
without realizing it.
Often a result is improved in a single step,
or with a small number of steps,
many fewer than the number needed to achieve convergence.
This is especially true with images where the dimensionality is huge
and where a simple improvement to the adjoint operator is sought.
Three-dimensional migration is an example.
In these cases it may be worthwhile to make some ad hoc improvements to
the gradient that acknowledge the gradient will be a perturbation
to the image and so should probably have
an amplitude and spectrum like that of .A more formal mathematical discussion of preconditioning
is on page .

** Next:** Why steepest descent is
** Up:** ITERATIVE METHODS
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Stanford Exploration Project

10/21/1998