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 eliminate 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
