solving an equation recursively
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Dear all,
I want to solve the following equation
m(t)=a(t)+k*m(t-1); t=2,...T
for the entire path m(t), with the initial condition
m(1)=a(1)+k*ee;
where ee=4;
In other words, If we solve the above equation, each m(t) will depend on past and current values of a's.
The vector a in the above equations is known, say a=randn(T,1) and k=0.4.
Any way of doing this?
Thank in advance
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Star Strider
2018-1-17
0 个投票
This seems to be homework, so I’ll not post the solution I coded.
6 个评论
Steven Lord
2018-1-17
That would work. I'd probably preallocate m, fill in the first value, and run the for loop from 2 to T.
m = zeros(1, T);
m(1) = a(1)+k*ee;
for t = 2:T
m(t) = a(t)+k*m(t-1);
end
That avoids having to check if the if condition is true during each iteration of the for loop body.
ektor
2018-1-17
Star Strider
2018-1-17
@Steven Lord — Thank you!
@Staf — Note that ‘a’ is determined completely before the loop, and according to your initial post, never changes. You can access the entire vector whenever you want to. The ‘m(t)’ assignment in the for loop stores all the values of the ‘m’ vector as the loop executes. You can access all of its values after the loop completes. So ‘m’ is already a function of the past and current values of ‘a’ in each iteration.
ektor
2018-1-17
Star Strider
2018-1-17
How does ‘a’ change in each iteration? You never mentioned that! I was using the information you provided.
You would create and update ‘a’ as ‘a(t)’ the same way you create and update ‘m(t)’, using whatever rule you want to create and define it it. Preallocate ‘a’ as well as ‘m’.
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