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Conjugate Gradient Methods
Conjugate Gradient Methods
2 selected
Difficulty 6-6
2 unseen
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Intermediate
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2 intermediate
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Question 1 of 2
120s
intermediate (6/10)
state theorem
CG with condition number
κ
=
λ
m
a
x
/
λ
m
i
n
has the convergence rate
∥
e
k
∥
A
≤
2
ρ
k
∥
e
0
∥
A
. What is
ρ
?
Hide and think first
A.
ρ
=
(
κ
−
1
)
/
(
κ
+
1
)
, with the *square root* of the condition number, beating steepest descent
B.
ρ
=
1/
κ
, an inverse-condition-number rate that becomes very fast for well-conditioned systems
C.
ρ
=
1/
κ
, faster than the standard CG rate, achieved when the spectrum of
A
is well-clustered
D.
ρ
=
(
κ
−
1
)
/
(
κ
+
1
)
, the same rate as steepest descent (CG matches GD on quadratics)
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