I mplement a MATLAB function secantBisection . Implement a MATLAB function secan

Question

Implement a MATLAB function secantBisection

. Implement a MATLAB function secantBisection of the form

function p=secantBisection(f,a,b,tol,N)

combining Secant method and the Bisection method according to the following procedure:

1. start with p = a; p1 = (a + b)/2;

2. Attempt a secant update step: p = p f(p) p1p f(p1)f(p) ;

3. If p is outside of [a, b], set p = p1;

4. If f(p)f(b) < 0, set a = p; otherwise set b = p;

5. Terminate if |f(p)| < tol;

6. Repeat from step 1, until maximal number of iteration is reached.

Run your function secantBisection using

f(x) = sin x e x on the interval [2, 12]: f = @(x) sin(x)-exp(-x); x = secantBisection(f,2,12,1e-6,100);

Present the result in a table showing for each iteration the method used (secant or bisection), a, b, p, and f(p).

Explanation / Answer

function root = bisect(f,a,b,tol,N)
%
% BISECT(f,a,b,tol,N)
% f string giving function name
% a,b     such that f(a)*f(b) < 0
% tol     positive tolerance
% N       number of steps

% check input data
fa = feval(f,a);
fb = feval(f,b);
if ( fa*fb > 0 )
   fprintf('input interval does not bracket ');
   return
end
if ( tol <= 0 )
   fprintf('tolerance must be positive ');
   return
end

% compute midpoint and evaluate function there
f(a) = p
p1 = (a + b)/2;
f(p1) = feval(f,p1);

p = (p-(f(p)*p1)-p*(f(p1)-f(p)))

If (p > fa * fb)
   p = p1;
   f(p) = f(p1);

% main loop
while 1
   If(f(p)*f(b) < 0)
     a = p;
    f(a) = f(p);
else
      b = p;
    f(b) = f(p);
    return
end

if (f(p) < tol)
return
end
  

    x : 9.452
  

Step x F(x) |x(i) - x(i-1)| x2 7.904 0.998 4.096 x3 10.567 -0.91 2.663 x4 9.297 0.127 1.270 x5 9.452 -0.028 0.156 x6 9.452 0 0.156

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