Approximating derivative and plotting error.

Hi, I'd sincerely appreciate it if someone were willing to review the few lines of code below and indicate why they don't quite yield the expected output.

I am asked to generate using MATLAB approximated values of f(x)=cos(x) at nodes x+h,x-h with random errors <=5*10^-6 (using rand ) for h=10^-8,10^-7,...,10^-1. Hence, f_approx(x+h)=f(x+h)+e(x+h) f_approx(x-h)=f(x-h)+e(x-h) where e(x)<=5*10^-6 in order to then find approximation for f'(1.2) by using the approximation: f'(x)=[f(x+h)-f(x-h)]/2h I am finally asked to plot the error with respect to the value of h.

Below is my code. I am not really sure why it yields one line across the y axis and another across the x axis.

h=(10^-1).^[1:8];
x=1.2;
fminush=cos(x-h)+(5e-6)*rand(1,1);
fplush=cos(x+h)+(5e-6)*rand(1,1);
fder=(fplush-fminush)./(2*h);
plot(h,abs(-sin(x)-fder))

Answer 1

[Shubham Mishra]

max_iter=50;

x0=1;

tolx= 1e-3;

x=x0;

xold=x0;

for i= 1:max_iter

f= (1-x)*exp(-2*x)-3*exp(-x)+2;

df= -2*(1-x)*exp(-2*x)-exp(-2*x)+3*exp(-x);

x= x-f/df;

err(i)= abs(x-xold);

xold=x;

if err(i)<tolx

break;

end

end

for i=1:8

err(i)=err(i)*1000

end

plot(err(i),i,'--r');