Question

Please, please use MATLAB and explain everything, thank you!!! If possible please plot the values.

Consider the general problem of finding a root of f, that is, find a solution to the equation f(x) = 0. The secant method: y = p(x) equiv f(x_1) + (x - x_1) middot f(x_1) - f(x_0)/x_1 - x_0 Implement the secant method for solving the problem of finding a solution to the equation x = cos x. Use your computer implementation of the secant method with initial guess x_0 = 1 to e_n = alpha - x_n, where alpha is the exact solution. Use alpha = 0.7390851332151607.

Answer 1

Solution: The MATLAB code for secant method is shown below: Enter function la-input ('Enter function:',s Store function f-inline (la) %Get first point x (1) -input ('Enter 1st point') 8Get second point x (2) -input ('Enter 2nd point :'); %Enter error value n-input ('Enter error allowed: ') Define liter lIter 0 for li-3:1000 %Compute x f (x (li-2) Update iteration lIter lIter+1; %If error condition matches if abs ((x (li)-x (li-1)) /x (li)) 100<n %Assign root root-x (li) store iteration count iteration-lIter %Break

break %End end %End end Sample Output: sh-4.3$ octave -qf-no-window-system demo.m Enter function: x-cos (x) Enter 1st point 0 Enter 2nd point1 Enter error allowed: 0.001 root0.73909 iteration = 5 sh-4.3s

code:

%Enter function

la=input('Enter function:','s');

%Store function

f=inline(la)

%Get first point

x(1)=input('Enter 1st point : ');

%Get second point

x(2)=input('Enter 2nd point : ');

%Enter error value

n=input('Enter error allowed: ');

%Define lIter

lIter=0;

%Loop

for li=3:1000

%Compute x

x(li) = x(li-1) - (f(x(li-1)))*((x(li-1) - x(li-2))/(f(x(li-1)) - f(x(li-2))));

  

   %Update iteration

    lIter=lIter+1;

   

    %If error condition matches

    if abs((x(li)-x(li-1))/x(li))*100<n

   

        %Assign root

        root=x(li)

       

        %Store iteration count

        iteration=lIter

       

        %Break

        break

       

    %End   

    end

   

%End   

end