<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
an	O
iterative	B-Algorithm
method	I-Algorithm
is	O
called	O
locally	B-Algorithm
convergent	I-Algorithm
if	O
the	O
successive	O
approximations	O
produced	O
by	O
the	O
method	O
are	O
guaranteed	O
to	O
converge	B-Algorithm
to	O
a	O
solution	O
when	O
the	O
initial	O
approximation	O
is	O
already	O
close	O
enough	O
to	O
the	O
solution	O
.	O
</s>
<s>
Iterative	B-Algorithm
methods	I-Algorithm
for	O
nonlinear	O
equations	O
and	O
their	O
systems	O
,	O
such	O
as	O
Newton	O
's	O
method	O
are	O
usually	O
only	O
locally	B-Algorithm
convergent	I-Algorithm
.	O
</s>
<s>
An	O
iterative	B-Algorithm
method	I-Algorithm
that	O
converges	O
for	O
an	O
arbitrary	O
initial	O
approximation	O
is	O
called	O
globally	O
convergent	O
.	O
</s>
<s>
Iterative	B-Algorithm
methods	I-Algorithm
for	O
systems	O
of	O
linear	O
equations	O
are	O
usually	O
globally	O
convergent	O
.	O
</s>
