Answer to Question #278313 in MatLAB for mani

Question

Find the root of the following equation using the Newton-Raphson method. Choose the initial guess as 𝑥 (0) = 10. Choose the error tolerance as tol=1e-6. In other words, the iterations should be stopped when the error i. Please report the value of x after 2 iterations ii. Please report the converged solution, where error is less than 1e-6. iii. Please report the number of iterations required to reach this converged solution

Answer 1

clc;
clear all;
close all;


% function 
f = @(x) x^2.5 + 23*x^1.5 -50*x + 1150;


% derivative
f_prime = @(x) 2.5*x^1.5 + 23*1.5*x^0.5 - 50;


% function for next iteration according to the Newton-Raphson method
g = @(x) x - f(x) / f_prime(x);


% tolerance
tol = 1e-6;


x_old = 10; % previous value of x
x = [x_old];  % array to store x after each iteration


x_new = g(x_old);  % new value of x


ii = 0;
while abs(x_new - x_old) > tol
    x_old = x_new;
    x_new = g(x_old);
    x = [x, x_new];  % append array with current iteration
end


fprintf('The value of x after 2 iterations: %f%+fj\n', real(x(3)), imag(x(3)))
fprintf('The converged solution: %f%+fj\n', real(f(x(end))), imag(f(x(end))))
fprintf('The number of iterations required to reach this converged solution: %i\n', length(x)-1)