<s>
Successive	B-Algorithm
parabolic	I-Algorithm
interpolation	I-Algorithm
is	O
a	O
technique	O
for	O
finding	O
the	O
extremum	O
(	O
minimum	O
or	O
maximum	O
)	O
of	O
a	O
continuous	O
unimodal	O
function	O
by	O
successively	O
fitting	O
parabolas	O
(	O
polynomials	O
of	O
degree	O
two	O
)	O
to	O
a	O
function	O
of	O
one	O
variable	O
at	O
three	O
unique	O
points	O
or	O
,	O
in	O
general	O
,	O
a	O
function	O
of	O
n	O
variables	O
at	O
1+n( n+3	O
)	O
/2	O
points	O
,	O
and	O
at	O
each	O
iteration	O
replacing	O
the	O
"	O
oldest	O
"	O
point	O
with	O
the	O
extremum	O
of	O
the	O
fitted	O
parabola	O
.	O
</s>
<s>
Only	O
function	O
values	O
are	O
used	O
,	O
and	O
when	O
this	O
method	O
converges	O
to	O
an	O
extremum	O
,	O
it	O
does	O
so	O
with	O
an	O
order	B-Architecture
of	I-Architecture
convergence	I-Architecture
of	O
approximately	O
1.325	O
.	O
</s>
<s>
The	O
superlinear	O
rate	B-Architecture
of	I-Architecture
convergence	I-Architecture
is	O
superior	O
to	O
that	O
of	O
other	O
methods	O
with	O
only	O
linear	B-Architecture
convergence	I-Architecture
(	O
such	O
as	O
line	B-Algorithm
search	I-Algorithm
)	O
.	O
</s>
<s>
Moreover	O
,	O
not	O
requiring	O
the	O
computation	O
or	O
approximation	O
of	O
function	O
derivatives	B-Algorithm
makes	O
successive	B-Algorithm
parabolic	I-Algorithm
interpolation	I-Algorithm
a	O
popular	O
alternative	O
to	O
other	O
methods	O
that	O
do	O
require	O
them	O
(	O
such	O
as	O
gradient	B-Algorithm
descent	I-Algorithm
and	O
Newton	B-Algorithm
's	I-Algorithm
method	I-Algorithm
)	O
.	O
</s>
<s>
Furthermore	O
,	O
if	O
function	O
derivatives	B-Algorithm
are	O
available	O
,	O
Newton	B-Algorithm
's	I-Algorithm
method	I-Algorithm
is	O
applicable	O
and	O
exhibits	O
quadratic	O
convergence	O
.	O
</s>
<s>
Alternating	O
the	O
parabolic	O
iterations	O
with	O
a	O
more	O
robust	O
method	O
(	O
golden	B-Algorithm
section	I-Algorithm
search	I-Algorithm
is	O
a	O
popular	O
choice	O
)	O
to	O
choose	O
candidates	O
can	O
greatly	O
increase	O
the	O
probability	O
of	O
convergence	O
without	O
hampering	O
the	O
convergence	B-Architecture
rate	I-Architecture
.	O
</s>
