Question

MATLAB code needed:

Use the newton's method to find the 37th root of 66453634 and show the number of iterations, ends of the interval and which will converge fastest falsi, secant or newtons method.

Answer 1

clc;

clear;

f = @(x) x^37-66453634;

g = @(x) 37*x^36;

xl=input('Enter the guess value:');

tol=input('Enter the allowed error:');

if g(xl)==0

    fprintf('The guess is incorrect! Enter new guesse\n');

    xl=input('Enter the guess value:');

end

for i=1:10000

xr=xl- f(xl)/g(xl);

if abs( xl-xr)<tol, break,end

if abs(f(xr))<abs(f(xl))

    xl=xr;

end

fprintf('Root after %i interation is: %d \n',i,xr);

end

fprintf('The required root  is:%d found after %d iterations',xr,i);

Among these, secant and newtons method will converge equally fast and faster than falsi.