how can we sketch the graph of this iteration xn+1=xn-8*f'(xn) in matlab code?

f(x)=x^2;

x0=0.5;

tolerance =0.0001

xn+1=xn-8*f'(xn)

[John D'Errico]

Will you post every homework assignment you get? Please don't. Please start to do your own homework.

Answer 1

[Cris LaPierre]

Have you tried the plot command?

See Ch 9 of MATLAB Onramp.

Answer 2

[Walter Roberson]

consider

f(x)=x^2;
x(n+1) = x(n) -8*f'(x(n))

But when f(x) = x^2 then f'(x) = 2*x so x(n+1) = x(n) - 8*2*x(n) = -15*x(n)

and so X(N) = (-15)^N * X0^N

When X0 > 1/15 then X0^N does not shrink faster than the 15^N grows so this equation is divergent for X0 as large as 1/2 and will be approximately (-8)^N