<s>
The	O
golden-section	B-Algorithm
search	I-Algorithm
is	O
a	O
technique	O
for	O
finding	O
an	O
extremum	O
(	O
minimum	O
or	O
maximum	O
)	O
of	O
a	O
function	O
inside	O
a	O
specified	O
interval	O
.	O
</s>
<s>
The	O
algorithm	O
is	O
the	O
limit	O
of	O
Fibonacci	B-Algorithm
search	I-Algorithm
(	O
also	O
described	O
below	O
)	O
for	O
many	O
function	O
evaluations	O
.	O
</s>
<s>
Fibonacci	B-Algorithm
search	I-Algorithm
and	O
golden-section	B-Algorithm
search	I-Algorithm
were	O
discovered	O
by	O
Kiefer	O
(	O
1953	O
)	O
(	O
see	O
also	O
Avriel	O
and	O
Wilde	O
(	O
1966	O
)	O
)	O
.	O
</s>
<s>
The	O
golden-section	B-Algorithm
search	I-Algorithm
is	O
an	O
efficient	O
way	O
to	O
progressively	O
reduce	O
the	O
interval	O
locating	O
the	O
minimum	O
.	O
</s>
<s>
The	O
golden-section	B-Algorithm
search	I-Algorithm
requires	O
that	O
these	O
intervals	O
be	O
equal	O
.	O
</s>
<s>
The	O
golden-section	B-Algorithm
search	I-Algorithm
chooses	O
the	O
spacing	O
between	O
these	O
points	O
in	O
such	O
a	O
way	O
that	O
these	O
points	O
have	O
the	O
same	O
proportion	O
of	O
spacing	O
as	O
the	O
subsequent	O
triple	O
or	O
.	O
</s>
<s>
In	O
order	O
to	O
approximate	O
the	O
probe	O
positions	O
of	O
golden	B-Algorithm
section	I-Algorithm
search	I-Algorithm
while	O
probing	O
only	O
integer	O
sequence	O
indices	O
,	O
the	O
variant	O
of	O
the	O
algorithm	O
for	O
this	O
case	O
typically	O
maintains	O
a	O
bracketing	O
of	O
the	O
solution	O
in	O
which	O
the	O
length	O
of	O
the	O
bracketed	O
interval	O
is	O
a	O
Fibonacci	B-Algorithm
number	I-Algorithm
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
the	O
sequence	O
variant	O
of	O
golden	B-Algorithm
section	I-Algorithm
search	I-Algorithm
is	O
often	O
called	O
Fibonacci	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
Fibonacci	B-Algorithm
search	I-Algorithm
was	O
first	O
devised	O
by	O
Kiefer	O
(	O
1953	O
)	O
as	O
a	O
minimax	B-Algorithm
search	O
for	O
the	O
maximum	O
(	O
minimum	O
)	O
of	O
a	O
unimodal	O
function	O
in	O
an	O
interval	O
.	O
</s>
