In applied mathematics, **symmetric successive overrelaxation (SSOR)**, is a preconditioner.

If the original matrix can be decomposed into diagonal, lower and upper tridiagonal as
A
=
D
+
L
+
L
T
then SSOR preconditioner matrix is defined as

M
=
(
D
+
L
)
D
−
1
(
D
+
L
)
T
It can also be parametrised by
ω
as follows.

M
(
ω
)
=
ω
2
−
ω
(
1
ω
D
+
L
)
(
D
)
−
1
(
1
ω
D
+
L
)
T