Lecture2 Matlab

Bisection Algorithm

To ?nd a solution to f (x) = 0 given the continuous function f on the interval [a, b], where f (a) and f (b) have opposite signs:

INPUT endpoints a, b; ?, and maximum number of iterations n.
OUTPUT approximate solution p or message of failure.

Bisection Algorithm:
Step 1 input i =1:n, a, b;
Step 2 Set pi = (bi + ai)/2;
Step 3 If f(p) = 0 or (b ? a) < ?, then
OUTPUT (pi); (Procedure completed successfully.)
STOP.
Step 4 Set i = i + 1.
Step 5 If f(a) · f(p) < 0 then set b = p;
else set a = p.
Step 6 OUTPUT (‘Method failed after n iterations);
STOP.
Bisection Algorithm

To ?nd a solution to f (x) = 0 given the continuous function f on the interval [a, b], where f (a) and f (b) have opposite signs:

INPUT endpoints a, b; ?, and maximum number of iterations n.
OUTPUT approximate solution p or message of failure.

Bisection Algorithm:
Step 1 input i =1:n, a, b;
Step 2 Set pi = (bi + ai)/2;
Step 3 If f(p) = 0 or (b ? a) < ?, then
OUTPUT (pi); (Procedure completed successfully.)
STOP.
Step 4 Set i = i + 1.
Step 5 If f(a) · f(p) < 0 then set b = p;
else set a = p.
Step 6 OUTPUT (‘Method failed after n iterations);
STOP.