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Newton-Raphson method

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Alexa Fernanda Cantú García
Answered: Monisha Nalluru on 11 Jan 2021
I have the function f(x)=sen(x)-2x^2 with x0=1.1 and iterating until the approximate relative error (Ea) is less than the estimated error Es=0.02%. The exact value of the root is 0.4810 and I need to get the find the percent true relative error (Ev).
This is what i have done, but it doesn't run with the trigonometric function.
%This program is for you to run it, is problem 2 of HW1.
f=@(x) x.^3-(12.1*x.^2)+(45.86*x)-52.976 %f(x) of Problem 2
x0=input("Enter x0_");%Your initial "x"
EE=input("Enter EE__");%your Absolute relative approximated percentage error
vv=input("Enter vv_");%Is the true value, the real known root
nrhw1(f,x0,EE,vv)

Answers (1)

Monisha Nalluru
Monisha Nalluru on 11 Jan 2021
Relative error is used in Newton Raphson method inorder to find whther the root matches the given tolerance.
Relative error can bee found using the following formula relative_error = abs( f(x+1) -f(x)/f(x+1)) * 100
As an example
function [r] = newton(x1)
n = 1000;
tol_error = 0.0002;
r = x1;
for t=1:n
x_plus = x1 - (my_func(x1)/my_func_diff(x1));
relative_error(t) = abs((x_plus - x1)/(x_plus))*100; % calculating relative error
disp(relative_error(t));
fun_val(t) = my_func(x1);
if (relative_error(t) < tol_error) % checking whether relative error is less than tolerance
display(approx_error(t));
r = x_plus;
break;
else
x1 = x_plus;
end
end
end
function y = my_func_diff(x)
y = cos(x)-4*x;
end
function y = my_func(x)
y = sin(x)-2*x^2;
end
Hope this helps!

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