How to solve this equation
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Hi,everyone,there is a equation as followed:
f(x)=h0*f(x)+h1*f(x-1)+h2*f(x-2)+h3*f(x-3);
The values of the h0~h3 are given,then how to solve this equation?
thank you!
1 个评论
Geoff
2012-3-26
This equation looks intractably recursive. Are those f(x) terms on the right-hand side in fact supposed to be some other function/dataset, such as g(x)?
采纳的回答
Walter Roberson
2012-3-26
You need three values of f(x) in order to completely solve the equation.
Or it can be expressed in terms of the known constants together with the unknown f(0), f(1), f(2)
sum(-((h0 - 1 + R .* h1 + h2 * R.^2) .* f(0) + R .* ((h0 - 1 + R .* h1) .* f(1) + R .* f(2) .* (h0 - 1))) .* (1./R)^x ./ (3 * h3 .* R.^3 + 2 * h2 .* R.^2 + R * h1)
where
R = roots([h3, h2, h1, h0-1]);
Note: all three roots of R must be included, even if imaginary!
更多回答（1 个）
Stefan Wehmeier
2012-3-26
This is a recurrence equation and thus has to declared as such using rec(...).
eq = evalin(symengine, 'rec(f(x)=h0*f(x)+h1*f(x-1)+h2*f(x-2)+h3*f(x-3), f(x))');
solve(eq)
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