Often called the method of Bolzano. If there are signs of change in function on the interval, then the function value is calculated at the midpoint. Then the root location is determined at the midpoint of the interval where the sign changes.
The first stage of this process is to establish the value of a and b as a boundary segment of the value of unknown function. Limits a and b give you a price for the function f (x) for x = a and x = b. The next step is to check whether f (a). F (b) <0.
If these conditions are fulfilled, then there is the function of roots in this segment. If not, return must set the value of a and b so that in accordance with the multiplication of f (a) x f(b) <0.
With the formula m = (a + b) / 2, checked whether the absolute value of f (m) <10-6 (margin of error deviation). If true, the value of x = m is the solution sought. If not met, set new limits by changing the value of b = m if f (a) * f (m) <0, and replace if m = f (a) xf (m)> 0; the process of discovering new m done with the procedure has been described.
Looking back to the drawing below:
given f (x) = 0; continuous nature and limits of the interval [a, b], f (a) f (b) <= 0
The first stage of this process is to establish the value of a and b as a boundary segment of the value of unknown function. Limits a and b give you a price for the function f (x) for x = a and x = b. The next step is to check whether f (a). F (b) <0.
If these conditions are fulfilled, then there is the function of roots in this segment. If not, return must set the value of a and b so that in accordance with the multiplication of f (a) x f(b) <0.
With the formula m = (a + b) / 2, checked whether the absolute value of f (m) <10-6 (margin of error deviation). If true, the value of x = m is the solution sought. If not met, set new limits by changing the value of b = m if f (a) * f (m) <0, and replace if m = f (a) xf (m)> 0; the process of discovering new m done with the procedure has been described.
Looking back to the drawing below:
given f (x) = 0; continuous nature and limits of the interval [a, b], f (a) f (b) <= 0
Figure 1. Determination of the midpoint m interval Bisection method