I have an iterative sum from $k=0$ to $k=n$ where the resulting sum is a polynomial of degree $n$.
I want to find the numerical root of this polynomial using FindRoot, starting from $x_0$ where the root I'm interested in is converging to some value. However I only know this $x_0$ for small $n \sim 60$.
Then FindRoot will give me a more precise $x_0$ and I can use this to find the root for $n=65$. I then use this root as my $x_0$ for $n=70$ etc. etc.
However I can only really increase $n$ by $5$ each time as I don't know where the root is converging and if I increase $n$ by more, FindRoot starts finding other roots which I know aren't the value I'm looking for.
How I can set it up so that I can run to $n=300$, for example, where FindRoot will use the root found $5$ iterations ago as its $x_0$?
Here's a sample:
max=90;
f[[0]]=1;
For[n=1,n<=max,n=n+1,
f[[n]]=Sum[f[[k]]Coefficient[S,y^k],{k,0,n}]];
MySum=Sum[f[[i]],{i,0,max}]
FindRoot[MySum ,{x,x_0},WorkingPrecision->7]
where $S$ is some polynomial $S(x,y)$
x_0
? I don't think that's what you want. $\endgroup$ – RunnyKine Aug 20 '14 at 11:43