<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
Estrin	B-Algorithm
's	I-Algorithm
scheme	I-Algorithm
(	O
after	O
Gerald	O
Estrin	O
)	O
,	O
also	O
known	O
as	O
Estrin	O
's	O
method	O
,	O
is	O
an	O
algorithm	O
for	O
numerical	B-General_Concept
evaluation	I-General_Concept
of	O
polynomials	O
.	O
</s>
<s>
Horner	O
's	O
method	O
for	O
evaluation	O
of	O
polynomials	O
is	O
one	O
of	O
the	O
most	O
commonly	O
used	O
algorithms	O
for	O
this	O
purpose	O
,	O
and	O
unlike	O
Estrin	B-Algorithm
's	I-Algorithm
scheme	I-Algorithm
it	O
is	O
optimal	O
in	O
the	O
sense	O
that	O
it	O
minimizes	O
the	O
number	O
of	O
multiplications	O
and	O
additions	O
required	O
to	O
evaluate	O
an	O
arbitrary	O
polynomial	O
.	O
</s>
<s>
Estrin	B-Algorithm
's	I-Algorithm
scheme	I-Algorithm
is	O
one	O
method	O
that	O
attempts	O
to	O
overcome	O
this	O
serialization	O
while	O
still	O
being	O
reasonably	O
close	O
to	O
optimal	O
.	O
</s>
<s>
Estrin	B-Algorithm
's	I-Algorithm
scheme	I-Algorithm
operates	O
recursively	O
,	O
converting	O
a	O
degree-n	O
polynomial	O
in	O
x	O
(	O
for	O
n≥2	O
)	O
to	O
a	O
degree	O
-	O
polynomial	O
in	O
x2	O
using	O
independent	O
operations	O
(	O
plus	O
one	O
to	O
compute	O
x2	O
)	O
.	O
</s>
<s>
They	O
may	O
also	O
be	O
evaluated	O
using	O
a	O
native	O
multiply	B-Algorithm
–	I-Algorithm
accumulate	I-Algorithm
instruction	O
on	O
some	O
architectures	O
,	O
an	O
advantage	O
that	O
is	O
shared	O
with	O
Horner	O
's	O
method	O
.	O
</s>
<s>
Repeating	O
this	O
+1	O
times	O
,	O
one	O
arrives	O
at	O
Estrin	B-Algorithm
's	I-Algorithm
scheme	I-Algorithm
for	O
parallel	O
evaluation	O
of	O
a	O
polynomial	O
:	O
</s>
<s>
Evaluate	O
Q(y )	O
=	O
D0	O
+	O
D1y	O
+	O
D2y2	O
+	O
⋯	O
+	O
Dy	O
using	O
Estrin	B-Algorithm
's	I-Algorithm
scheme	I-Algorithm
.	O
</s>
<s>
This	O
performs	O
a	O
total	O
of	O
n	O
multiply-accumulate	B-Algorithm
operations	I-Algorithm
(	O
the	O
same	O
as	O
Horner	O
's	O
method	O
)	O
in	O
line	O
1	O
,	O
and	O
an	O
additional	O
squarings	O
in	O
line	O
3	O
.	O
</s>
<s>
Written	O
with	O
Estrin	B-Algorithm
's	I-Algorithm
scheme	I-Algorithm
we	O
have	O
:	O
</s>
