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