How to solve this equation
1 visualización (últimos 30 días)
Mostrar comentarios más antiguos
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 comentario
Geoff
el 26 de Mzo. de 2012
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)?
Respuesta aceptada
Walter Roberson
el 26 de Mzo. de 2012
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!
0 comentarios
Más respuestas (1)
Stefan Wehmeier
el 26 de Mzo. de 2012
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)
0 comentarios
Ver también
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!