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,
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(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
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