<s>
Modified	B-Algorithm
Richardson	I-Algorithm
iteration	I-Algorithm
is	O
an	O
iterative	B-Algorithm
method	I-Algorithm
for	O
solving	O
a	O
system	O
of	O
linear	O
equations	O
.	O
</s>
<s>
Richardson	B-Algorithm
iteration	I-Algorithm
was	O
proposed	O
by	O
Lewis	O
Fry	O
Richardson	O
in	O
his	O
work	O
dated	O
1910	O
.	O
</s>
<s>
It	O
is	O
similar	O
to	O
the	O
Jacobi	B-Algorithm
and	O
Gauss	B-Algorithm
–	I-Algorithm
Seidel	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Suppose	O
that	O
is	O
symmetric	B-Algorithm
positive	I-Algorithm
definite	I-Algorithm
and	O
that	O
are	O
the	O
eigenvalues	O
of	O
.	O
</s>
<s>
The	O
optimal	O
choice	O
,	O
minimizing	O
all	O
,	O
is	O
,	O
which	O
gives	O
the	O
simplest	O
Chebyshev	B-Algorithm
iteration	I-Algorithm
.	O
</s>
<s>
where	O
is	O
the	O
condition	B-Algorithm
number	I-Algorithm
.	O
</s>
<s>
Because	O
of	O
the	O
form	O
of	O
A	O
,	O
it	O
is	O
a	O
positive	B-Algorithm
semi-definite	I-Algorithm
matrix	I-Algorithm
,	O
so	O
it	O
has	O
no	O
negative	O
eigenvalues	O
.	O
</s>
<s>
which	O
is	O
equivalent	O
to	O
the	O
Richardson	B-Algorithm
iteration	I-Algorithm
by	O
making	O
.	O
</s>
