Find the cube root of 25 to four decimal places, using: The midpoint method The

Question

Find the cube root of 25 to four decimal places, using: The midpoint method The secant method (two-point recursion) Regula falsi Newton's method Aitken's method to improve the worst of the linear methods Find the cube root of 25 to four decimal places, using: The midpoint method The secant method (two-point recursion) Regula falsi Newton's method Aitken's method to improve the worst of the linear methods The midpoint method The secant method (two-point recursion) Regula falsi Newton's method Aitken's method to improve the worst of the linear methods

Explanation / Answer

%%%%%%%%%%%% Matlab code

clc;
clear all;
close all;
format long;

syms x
f=x^3-25;
tol=0.0001;

% % % bisection method
disp('Bisection method :');
a=0;
b=3;
for n=1:100;
    l1=subs(f,a);
    l2=subs(f,b);
  
    c(n)=(a+b)/2;
    l3=subs(f,c(n));
    if (n>2)
        if (abs( c(n)-c(n-1))< tol)
        break;
        end
    end
  
    if ( l3 < 0 )
        a=c(n);
    else
        b=c(n);
    end

end
fprintf('cube roots of 25 is : %f ', c(end) );

% %%% Secant method
y(1)=0;
y(2)=3;

disp('Secant method');
for n=2:100
    f1=subs(f,y(n));
    f2=subs(f,y(n-1));
    y(n+1)=y(n)-f1*(y(n)-y(n-1))/(f1-f2);
    err=abs(y(n+1)-y(n));
    if ( err < tol)
        break;
    end
end
fprintf('cube roots of 25 is : %f ', y(n+1) );

%%%Regula False Position method
disp('Regula False-position method ');
%

y(1)=0;
y(2)=3;
for n=2:100
    f1=subs(f,y(n));
    f2=subs(f,y(n-1));
    y(n+1)=(y(n-1)*f1-y(n)*f2)/(f1-f2);
    if ( abs(y(n+1)-y(n)) < tol)
        break;
    end
end
fprintf('cube roots of 25 is : %f ', y(n+1) );

% % % % N-R Method
disp('Newton Raphson method');
s(1)=3;
for n=1:100
    l1=subs(f,s(n));
    l2=subs(diff(f),s(n));
    s(n+1)=s(n)-l1/l2;
    e=abs(s(n+1)-s(n));
    if (e < tol)
        break;
    end
end
fprintf('cube roots of 25 is : %f ', s(end) );

OUTPUT:

Bisection method :
cube roots of 25 is : 2.924103
Secant method
cube roots of 25 is : 2.924018
Regula False-position method
cube roots of 25 is : 2.924018
Newton Raphson method
cube roots of 25 is : 2.924018

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