<s>
The	O
Jenkins	B-Algorithm
–	I-Algorithm
Traub	I-Algorithm
algorithm	I-Algorithm
for	O
polynomial	O
zeros	O
is	O
a	O
fast	O
globally	O
convergent	O
iterative	O
polynomial	O
root-finding	O
method	O
published	O
in	O
1970	O
by	O
Michael	O
A	O
.	O
Jenkins	O
and	O
Joseph	O
F	O
.	O
Traub	O
.	O
</s>
<s>
The	O
Jenkins	B-Algorithm
–	I-Algorithm
Traub	I-Algorithm
algorithm	I-Algorithm
has	O
stimulated	O
considerable	O
research	O
on	O
theory	O
and	O
software	O
for	O
methods	O
of	O
this	O
type	O
.	O
</s>
<s>
The	O
Jenkins	B-Algorithm
–	I-Algorithm
Traub	I-Algorithm
algorithm	I-Algorithm
calculates	O
all	O
of	O
the	O
roots	O
of	O
a	O
polynomial	O
with	O
complex	O
coefficients	O
.	O
</s>
<s>
Furthermore	O
,	O
the	O
convergence	O
is	O
slightly	O
faster	O
than	O
the	O
quadratic	B-Architecture
convergence	I-Architecture
of	O
Newton	O
–	O
Raphson	O
iteration	O
,	O
however	O
,	O
it	O
uses	O
at	O
least	O
twice	O
as	O
many	O
operations	O
per	O
step	O
.	O
</s>
<s>
giving	O
rise	O
to	O
a	O
higher	O
than	O
quadratic	B-Architecture
convergence	I-Architecture
order	O
of	O
,	O
where	O
is	O
the	O
golden	O
ratio	O
.	O
</s>
<s>
The	O
Jenkins	B-Algorithm
–	I-Algorithm
Traub	I-Algorithm
algorithm	I-Algorithm
described	O
earlier	O
works	O
for	O
polynomials	O
with	O
complex	O
coefficients	O
.	O
</s>
<s>
The	O
real	O
algorithm	O
always	O
converges	O
and	O
the	O
rate	B-Architecture
of	I-Architecture
convergence	I-Architecture
is	O
greater	O
than	O
second	O
order	O
.	O
</s>
<s>
The	O
software	O
for	O
the	O
Jenkins	B-Algorithm
–	I-Algorithm
Traub	I-Algorithm
algorithm	I-Algorithm
was	O
published	O
as	O
Jenkins	O
and	O
Traub	O
.	O
</s>
<s>
As	O
predicted	O
they	O
enjoy	O
faster	O
than	O
quadratic	B-Architecture
convergence	I-Architecture
for	O
all	O
distributions	O
of	O
zeros	O
.	O
</s>
