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From: landon donovan on 12 May 2010 00:36
Im using the next function to generate vectors according to the equation:
x(i+1)=x(i) + 3*x(i)^2 - 2*x(i)^3 + 0.5*x(i-1)

function [M] = generate(n)
x1=rand(30,1);
x2=rand(30,1);
M(:,1)=x1;
M(:,2)=x2;
for i=2:n-1
M(:,i+1)=M(:,i)+3*(M(:,i)).^2-2*(M(:,i)).^3+0.5*M(:,i-1);
end

but when I try n=100 , the last 94 columns of M result in NaN. Is this normal when the entries of the column are of order 1e-100000... ? That is, too very small; or too big of the order 1e100000... ? or am I commiting some error?
Please Help
From: Bruno Luong on 12 May 2010 01:53
"landon donovan" <lutobu(a)gmail.com> wrote in message <hsdb7j$mj9$1(a)fred.mathworks.com>...
> Im using the next function to generate vectors according to the equation:
> x(i+1)=x(i) + 3*x(i)^2 - 2*x(i)^3 + 0.5*x(i-1)
>
> function [M] = generate(n)
> x1=rand(30,1);
> x2=rand(30,1);
> M(:,1)=x1;
> M(:,2)=x2;
> for i=2:n-1
> M(:,i+1)=M(:,i)+3*(M(:,i)).^2-2*(M(:,i)).^3+0.5*M(:,i-1);
> end
>
> but when I try n=100 , the last 94 columns of M result in NaN. Is this normal when the entries of the column are of order 1e-100000... ? That is, too very small; or too big of the order 1e100000... ? or am I commiting some error?
> Please Help

Haven't tried your code, but it looks like the recursive scheme is unstable. That's why people spending their time studying stability, convergence, ...

Bruno
From: James Tursa on 12 May 2010 02:11
"landon donovan" <lutobu(a)gmail.com> wrote in message <hsdb7j$mj9$1(a)fred.mathworks.com>...
> Im using the next function to generate vectors according to the equation:
> x(i+1)=x(i) + 3*x(i)^2 - 2*x(i)^3 + 0.5*x(i-1)
>
> function [M] = generate(n)
> x1=rand(30,1);
> x2=rand(30,1);
> M(:,1)=x1;
> M(:,2)=x2;
> for i=2:n-1
> M(:,i+1)=M(:,i)+3*(M(:,i)).^2-2*(M(:,i)).^3+0.5*M(:,i-1);
> end
>
> but when I try n=100 , the last 94 columns of M result in NaN. Is this normal when the entries of the column are of order 1e-100000... ? That is, too very small; or too big of the order 1e100000... ? or am I commiting some error?

The individual pieces of your polynomial are becoming very large. Eventually they become too large for a finite value and become Infinity. And then at some point you do an Infinity - Infinity calculation and the result is NaN. This is not a stable way to generate whatever you are trying to generate.

James Tursa
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