<s>
The	O
Gauss	B-Algorithm
–	I-Algorithm
Newton	I-Algorithm
algorithm	I-Algorithm
is	O
used	O
to	O
solve	O
non-linear	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
problems	O
,	O
which	O
is	O
equivalent	O
to	O
minimizing	O
a	O
sum	O
of	O
squared	O
function	O
values	O
.	O
</s>
<s>
It	O
is	O
an	O
extension	O
of	O
Newton	B-Algorithm
's	I-Algorithm
method	I-Algorithm
for	O
finding	O
a	O
minimum	O
of	O
a	O
non-linear	O
function	O
.	O
</s>
<s>
Since	O
a	O
sum	O
of	O
squares	O
must	O
be	O
nonnegative	O
,	O
the	O
algorithm	O
can	O
be	O
viewed	O
as	O
using	O
Newton	B-Algorithm
's	I-Algorithm
method	I-Algorithm
to	O
iteratively	B-Algorithm
approximate	O
zeroes	O
of	O
the	O
components	O
of	O
the	O
sum	O
,	O
and	O
thus	O
minimizing	O
the	O
sum	O
.	O
</s>
<s>
Non-linear	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
problems	O
arise	O
,	O
for	O
instance	O
,	O
in	O
non-linear	O
regression	O
,	O
where	O
parameters	O
in	O
a	O
model	O
are	O
sought	O
such	O
that	O
the	O
model	O
is	O
in	O
good	O
agreement	O
with	O
available	O
observations	O
.	O
</s>
<s>
which	O
is	O
a	O
direct	O
generalization	O
of	O
Newton	B-Algorithm
's	I-Algorithm
method	I-Algorithm
in	O
one	O
dimension	O
.	O
</s>
<s>
Note	O
that	O
is	O
the	O
left	O
pseudoinverse	B-Algorithm
of	O
.	O
</s>
