1
Lecture10
Theorems 5.2 and 5.3
Algorithms 5.1, 5.2
Theorem 5.2
Let
x
0
be any starting point and suppose that the sequence
{
x
k
} is generated by the conjugate direction algorithm. Then
1
,
,
0
for
0

=
=
k
i
p
r
i
T
k
K
and
x
k
is minimizer of
over the set
x
b
Ax
x
x
T
T

=
2
1
)
(
f
{
}
}
,
,
{

1
0
0

+
=
k
p
p
span
x
x
x
K
(3)
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