<s>
The	O
Davidon	B-Algorithm
–	I-Algorithm
Fletcher	I-Algorithm
–	I-Algorithm
Powell	I-Algorithm
formula	I-Algorithm
(	O
or	O
DFP	O
;	O
named	O
after	O
William	O
C	O
.	O
Davidon	O
,	O
Roger	O
Fletcher	O
,	O
and	O
Michael	O
J	O
.	O
D	O
.	O
Powell	O
)	O
finds	O
the	O
solution	O
to	O
the	O
secant	O
equation	O
that	O
is	O
closest	O
to	O
the	O
current	O
estimate	O
and	O
satisfies	O
the	O
curvature	O
condition	O
.	O
</s>
<s>
It	O
was	O
the	O
first	O
quasi-Newton	B-Algorithm
method	I-Algorithm
to	O
generalize	O
the	O
secant	O
method	O
to	O
a	O
multidimensional	O
problem	O
.	O
</s>
<s>
The	O
DFP	O
formula	O
finds	O
a	O
solution	O
that	O
is	O
symmetric	O
,	O
positive-definite	B-Algorithm
and	O
closest	O
to	O
the	O
current	O
approximate	O
value	O
of	O
:	O
</s>
<s>
and	O
is	O
a	O
symmetric	O
and	O
positive-definite	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
The	O
DFP	O
formula	O
is	O
quite	O
effective	O
,	O
but	O
it	O
was	O
soon	O
superseded	O
by	O
the	O
Broyden	B-Algorithm
–	I-Algorithm
Fletcher	I-Algorithm
–	I-Algorithm
Goldfarb	I-Algorithm
–	I-Algorithm
Shanno	I-Algorithm
formula	I-Algorithm
,	O
which	O
is	O
its	O
dual	O
(	O
interchanging	O
the	O
roles	O
of	O
y	O
and	O
s	O
)	O
.	O
</s>
