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What's the fastest way to program a matrix recursion in matlab?

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Rosi Marungu
Rosi Marungu 2015-11-12
评论： Walter Roberson 2015-11-13
The matrix-recursion of the n by n matrices Y_t looks like this:
<<chart-googleapis-com-chart-cht-tx-chl-Y_-t--A-20-2B-20--sum_-i-1---p--20B_-i-Y_-t-i.>>
A and B are given.
This is my attempt, but it runs slowly:
Y = zeros(n,n,T); %Going to fill the 3rd dimension for Y_t, t=1:T
Y(:,:,1:p) = initializingY
for t=(p+1):T
Y(:,:,t) = A;
for i=1:p
Y(:,:,t) = Y(:,:,t) + B(:,:,i)*Y(:,:,t-i);
end
end
Can you think of a more efficient way to do this?

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回答（1 个）

Mathias
Mathias 2015-11-12
Use matrix product!
This code is about 10 times faster on my computer
for t=(p+1):T
Y(:,:,t) = A + sum(Y(:,:,(t-p+1):t).*B, 3);
end
Regards
  2 个评论
Rosi Marungu
Rosi Marungu 2015-11-12
Unfortunately B also has an index. It is different for the lags from 1 to p. There is no functionality I know of to do matrix multiplication along the 3rd dimension.
Walter Roberson
Walter Roberson 2015-11-13
pagefun() can be used to do matrix multiplication along the third dimension

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