The matrix and vectors are layed out in a simple block column fashion.
The nodes are ordered in a natural order to minimize bandwidth
and hence interprocessor communication. The columns (
) of the upper
triangular portion of the symmetric matrix
are layed out in
blocks on the processors, the vector members (
) associated with the
columns of the matrix are put on the same processor. The matrix-vector
multiply
requires that the members of
the left hand side vector
, which are in the same row as
an array member
stored on another processor,
be communicated to carry out the
computation. The right hand side result
, then needs to be sent back
to the same processor that sent the left hand side
(because of the
symmetry of
) - so that the final result can be calculated.