Approximating derivative and plotting error.

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Yuval
Yuval on 7 Nov 2013
Answered: Shubham Mishra on 21 Nov 2020
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))

Answers (1)

Shubham Mishra
Shubham Mishra on 21 Nov 2020
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');

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