Geology Reference
In-Depth Information
Fig. 4.10 Conjugate
directions in CG minimization
d
j
Hd
i
¼
0
;
j
6
¼ i
ð
4
:
24
Þ
find the minimum along the search
direction. A full mathematical description of a robust line search algorithm such as
Brent
Then we can use a line search technique to
s Method, which uses inverse parabolic interpolation to perform the line
minimization, can be found in Press et al. [
73
].
'
4.4.2 Broyden
Fletcher
Goldfarb
Shanno Algorithm
-
-
-
The BFGS-based algorithm is a variable metric or quasi-Newton method. To
describe the approach, consider (
4.22
), a second-order Taylor expansion of qua-
dratic error function E(w) around the minimum point w
*
.
The location of the minimum can be determined directly by differentiating
(
4.22
):
Þ
¼H
ð
w
w
Þ
¼
g
r
E
ð
w
0
ð
4
:
25
Þ
to give an expression for the minimum w*
w
¼ w
H
1
g
ð
4
:
26
Þ
