This is a method to find the roots of a single variable function. \(f(a)\) and \(f(b)\) have opposite signs and you are basically finding the midpoint between a and b. And you do this iteratively until \(f(p)\) equals to zero or you reach the iteration limit you set.
INPUT endpoints a,b; tolerance TOL;maximum number of iterations
OUTPUT approximate solution p or message of failure
Step 1 set \\(i = 1\\);
\\(FA = f(a)\\)
Step 2 while i =< $N_{o}$ do Steps 3-6.
Step 3 Set \\(p = a + (b - a)/2\\); (Compute \\(p\_{i}\\))
\\(FP = f(p)\\)
Step 4 If FP = 0 or (b - a)/2 < TOL then
OUTPUT (\\(p\\)) (Procedure is completed, output the point p)
STOP
Step 5 Set \\(i = i + 1\\).
Step 6 If \\(FA\ \dot\ FP\\) > 0 then \\(a = p\\); (Compute \\(a\_{i}\\),
\\(b\_{i}\\))
\\(FA = FP\\)
else set \\(b = p\\). (\\(FA\\) is unchanged.)
Step 7 OUTPUT ('Method failed after \\(N\_{o}\\) iterations')
STOP