In this paper the Parallel Pipelining SOR (ppSOR) method and
a iterative linear equation solver that uses the ppSOR method is presented.
This method does not require to color nodes of the graph which is associated
with the coefficient matrix to be solved.
Also in this paper the experimental results on a distributed
memory parallel processor that is a NEC cenju-3 with 16 PEs
are presented.
As shown in this paper, the convergence property of ppSOR method
is as same as the multi-color method, and the experimental results
confirm it.
With the property, SOR acceleration works as well as on a single processor
or as the multi-color method.
The experimental results also confirms this, and up to 10 times
speed up on a 16 PE parallel processor was obtained compared to 
the block SOR method which also does not require to color nodes.
And we obtain almost same or a little improved performance compared to
the well known multi-color method.
Then with this method we can solve a linear equation without coloring
but a better performance.