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Old 10-15-2006, 06:03 AM   #1
Registered: Oct 2003
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an existing efficient matrix multiplication algorithm?

Hello everyone,

I am looking for an efficient way to implement matrix multiplication in C/C++. Are there any existing good ways?

The matrix is stored in an one-dimentional array.

thanks in advance,
Old 10-15-2006, 06:23 AM   #2
Registered: Jul 2004
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Square matrices or non square? It matters because if it only handles square matrices, it'll be much faster
Old 10-16-2006, 12:54 AM   #3
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If your matrix haven't any symmetry, then the multiplication
algorithm will be of O(N^2) complexity, i.e. multiplication
takes about N*N operations (it is 10000 operations if N=100).

Now look at FFT (Fast Fourier Transform).
Ordinary Discrete Fourier transformation (DFT) of N-dim. vector f[n] is
F[k] = Sum( f[n]*exp(-2*pi*I/N*k*n) ,  n=0..N-1 ),
where I*I = -1
and may be rewritten as multiplication of some square matrix M and f[n].
On the other hand FFT uses the symmetry of M and can be computed in
O( N*log(N) ) operations. If N=100, then N*log(N) ~ 664 and it's about
10-15 times faster in this case than DFT (log(x) is base-2 logarithm).

So, if your matrix is symmetric, then there may be effective algorithm.
If not - multiply as always.

P.S.: One of my friends offer to use a video card for vector operations,
because most of them allows to do this!
P.P.S.: All this is related to matrix-matrix multiplication as well.


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