Approximating derivative and plotting error.
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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))
回答（1 个）
Shubham Mishra
2020-11-21
0 个投票
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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2020-11-21
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