e consider the problem
(
Quadratic form minimum
). We propose to
construct the sequence
as follows.
Start with any
.
Suppose we are after step
so that
is already calculated. Evaluate the direction of decay
and
set
We chose a
to
minimize
and then
set
We perform the following calculations to complete the
recipe:
Therefore,
|
|
(Orthogonality of residues)
|
We substitute definition of
:
We collect the description of the
recursion:
We elliminate one matrix multiplication by multiplying the last equation by
and adding
:
The recursion starts from
and the results are
accumulated
The equation
would accumulate numerical errors. Hence, periodically one has to calculate
correct residual by
using
Algorithm
(Steepest descent) Start from any
.
Set
|
