similar matrix multiplication speed up

2011 6 20
4 个回答
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Hi,
I need to multiply many times matrices of the same type. Is there a way to speed this up:
M1^m*M2^m*...
where Mi = expm(alpha(i)*P) P being a matrix (hermitian). Already all Mi are precalculated and the main calculation cost of my problem now is the long matrix multiplication through all i.
Thanks

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更多回答（3 个）

Gary
Gary 2011-6-20

0 个投票

mtimesx might help to calculate the Mi matrices and its power but can it speed up the multiplication between Mi?
Thanks for the answer btw.
Teja Muppirala
Teja Muppirala 2011-6-20

0 个投票

You can combine all of those multiplications into one expression using the properties of the matrix exponential.
Compare these 3 expressions:
P = rand(3);
P = P*P';
format long
% These are all the same
expm(2*P)^7*expm(4*P)^7*expm(5*P)^7
expm(14*P)*expm(28*P)*expm(35*P)
expm(7*(2+4+5)*P)
Gary
Gary 2011-6-20

0 个投票

Sorry the expression given at the beginning was kind of stupid. The Mi matrices are of the form Mi=expm(P0+alpha(i)P1) where P0 and P1 are hermitian and most of all non commutative. I cannot combine the terms.

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