Use MatLab Write a simple program to compare the secant meth

Use MatLab.

Write a simple program to compare the secant method with Newton\'s method for finding a root of each function.

a) x^3 - 3x + 1 with x0 = 2

b) x^3 - 2sin(x) with x0 = 1/2

Use the x1 value from Newton\'s method as the second starting point for the secant method. Print out each iteration for both methods.

Solution

a)

b)

%newton method
x = 0.5;
Tl = 0.0000001;
count = 0;
dx=1; %to execute while loop
f=-0.83; % because f(0.5)=-0.83
fprintf(\'step x dx f(x)\ \')
fprintf(\'%3i %12.8f %12.8f %12.8f\ \',count,x,dx,f)
xVec=x;fVec=f;
while (dx > Tl || abs(f)>Tl)
count = count + 1;
fprime = 3*x^2 + 3;
xnew = x - (f/fprime); % compute the new value of x
dx=abs(x-xnew); % compute how much x has changed since last step
x = xnew;
f = x^3 - 2*sin(x); % compute the new value of f(x)
fprintf(\'%3i %12.8f %12.8f %12.8f\ \',count,x,dx,f) %this will print value of x, dx and fx in every iteration
%secant mathod
x(1)=input(\'Enter first point of guess interval: \');
x(2)=x %value from newton ethod

iteration=0;

for i=3:1000
x(i) = x(i-1) - (f(x(i-1)))*((x(i-1) - x(i-2))/(f(x(i-1)) - f(x(i-2))));
iteration=iteration+1;
if abs((x(i)-x(i-1))/x(i))*100<n
root=x(i)
iteration=iteration
break
end
end
end