•Matrix multiplications either with a vector or another
matrix are important cases where parallel
computing becomes necessary.
•This happens when the size of the matrix becomes very large.
•For a NxN matrix one needs N2 elements.
•For example for a complex matrix in double
precision one requires 16 N2 bytes
•
of memory.
•A matrix – vector multiplication takes N multiplications
and N – 1 additions while a matrix – matrix
multiplication takes N3 multiplications
and N3 – N2 additions.
•If the numbers are complex each multiplication 4 real
multiplications and two additions while
each addition is 2 real additions.
•On a 324 lattice even the simplest algorithm involves
5 billion double precision multiplications per sweep of the
lattice and one needs thousands of
sweeps.