similar matrix multiplication speed up

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

Answer 1

[Paulo Silva]

Try MTIMESX - Fast Matrix Multiply with Multi-Dimensional Support by James Tursa

Answer 2

[Gary]

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.

[Paulo Silva]

Sorry but I can't help further, never used it.

Answer 3

[Teja Muppirala]

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)

Answer 4

[Gary]

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.