<s>
In	O
numerical	O
linear	O
algebra	O
,	O
the	O
Jacobi	B-Algorithm
method	I-Algorithm
(	O
a.k.a.	O
</s>
<s>
the	O
Jacobi	B-Algorithm
iteration	I-Algorithm
method	O
)	O
is	O
an	O
iterative	O
algorithm	O
for	O
determining	O
the	O
solutions	O
of	O
a	O
strictly	B-Algorithm
diagonally	I-Algorithm
dominant	I-Algorithm
system	O
of	O
linear	O
equations	O
.	O
</s>
<s>
Each	O
diagonal	B-Algorithm
element	O
is	O
solved	O
for	O
,	O
and	O
an	O
approximate	O
value	O
is	O
plugged	O
in	O
.	O
</s>
<s>
When	O
and	O
are	O
known	O
,	O
and	O
is	O
unknown	O
,	O
we	O
can	O
use	O
the	O
Jacobi	B-Algorithm
method	I-Algorithm
to	O
approximate	O
.	O
</s>
<s>
Unlike	O
the	O
Gauss	B-Algorithm
–	I-Algorithm
Seidel	I-Algorithm
method	I-Algorithm
,	O
we	O
ca	O
n't	O
overwrite	O
with	O
,	O
as	O
that	O
value	O
will	O
be	O
needed	O
by	O
the	O
rest	O
of	O
the	O
computation	O
.	O
</s>
<s>
A	O
sufficient	O
(	O
but	O
not	O
necessary	O
)	O
condition	O
for	O
the	O
method	O
to	O
converge	O
is	O
that	O
the	O
matrix	O
A	O
is	O
strictly	O
or	O
irreducibly	O
diagonally	B-Algorithm
dominant	I-Algorithm
.	O
</s>
<s>
Strict	O
row	O
diagonal	B-Algorithm
dominance	I-Algorithm
means	O
that	O
for	O
each	O
row	O
,	O
the	O
absolute	O
value	O
of	O
the	O
diagonal	B-Algorithm
term	O
is	O
greater	O
than	O
the	O
sum	O
of	O
absolute	O
values	O
of	O
other	O
terms	O
:	O
</s>
<s>
The	O
Jacobi	B-Algorithm
method	I-Algorithm
sometimes	O
converges	O
even	O
if	O
these	O
conditions	O
are	O
not	O
satisfied	O
.	O
</s>
<s>
Note	O
that	O
the	O
Jacobi	B-Algorithm
method	I-Algorithm
does	O
not	O
converge	O
for	O
every	O
symmetric	O
positive-definite	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
In	O
case	O
that	O
the	O
system	O
matrix	O
is	O
of	O
symmetric	O
positive-definite	B-Algorithm
type	O
one	O
can	O
show	O
convergence	O
.	O
</s>
