<s>
The	O
Truncated	B-Algorithm
Newton	I-Algorithm
Method	I-Algorithm
originated	O
in	O
a	O
paper	O
by	O
Ron	O
Dembo	O
and	O
Trond	O
Steihaug	O
first	O
published	O
in	O
Mathematical	O
Programming	O
(	O
Dembo	O
,	O
R.S.	O
,	O
Steihaug	O
,	O
T	O
.	O
Truncated-Newton	O
algorithms	O
for	O
large-scale	O
unconstrained	O
optimization	O
.	O
</s>
<s>
Also	O
known	O
as	O
Hessian-free	B-Algorithm
optimization	I-Algorithm
,	O
are	O
a	O
family	O
of	O
optimization	O
algorithms	O
designed	O
for	O
optimizing	O
non-linear	O
functions	O
with	O
large	O
numbers	O
of	O
independent	O
variables	O
.	O
</s>
<s>
A	O
truncated	B-Algorithm
Newton	I-Algorithm
method	I-Algorithm
consists	O
of	O
repeated	O
application	O
of	O
an	O
iterative	O
optimization	O
algorithm	O
to	O
approximately	O
solve	O
Newton	B-Algorithm
's	I-Algorithm
equations	I-Algorithm
,	O
to	O
determine	O
an	O
update	O
to	O
the	O
function	O
's	O
parameters	O
.	O
</s>
<s>
It	O
follows	O
that	O
,	O
for	O
truncated	B-Algorithm
Newton	I-Algorithm
methods	I-Algorithm
to	O
work	O
,	O
the	O
inner	O
solver	O
needs	O
to	O
produce	O
a	O
good	O
approximation	O
in	O
a	O
finite	O
number	O
of	O
iterations	O
;	O
conjugate	B-Algorithm
gradient	I-Algorithm
has	O
been	O
suggested	O
and	O
evaluated	O
as	O
a	O
candidate	O
inner	O
loop	O
.	O
</s>
