Halving method - declaration and implementation

12-09  Source: Network gathering  Views:1 

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Halving method - declaration and implementation

A calculator simplifies the bisection method.

Declaration of halving method

Often in mathematics zeros of a function are calculated. As long as a zero at the same time is not a high or low spot, zeros are characterized in that the y-values ​​on the one hand are larger and less on the other side as zero. This is the basis for the Declaration of halving process. So is the procedure:

  1. In the bisection method, two x-values ​​are wanted, with an associated y value is positive and one is negative.
  2. If these values ​​are found, the average of the two x-values ​​is used in the function.
  3. If the result is positive, the x-value, which includes the negative y-value is used. Otherwise, the other x-value is used in the following.
  4. Now again the mean value of the mean value of the point 2 and the to be used in x-value is formed and also used in the function.
  5. This procedure is repeatedly carried out successively until the zero point is found.

Since the best explanation is always an example, followed by a calculation example of the halving method.

Example for implementation of the method halving

  1. As an example, the function f (x) = -2x + 4.5 is given. Put x = 0 and you will get the corresponding y-value 4.5.
  2. Due to the negative slope and the positive y-intercept of the line you can see that you can get a negative y-value for a positive x value.
  3. So put an for x the number. 3 This will give you the corresponding y-value -1.2. Thus, the actual zero between these x-values ​​must occur.
  4. The mean value between 0 and 3 is 1.5. Set this value so in the function. This will give you the corresponding y-value of 1.8.
  5. The zero point should be between the points (1.5 / 1.8) and (3 / 1.2) are. thus forming the mean value between 1.5 and 3. It is situated at 2.25.
  6. Put 2.25 in the function and you will receive 0 for the y value. Thus your zero is (2.25 / 0)

Other possible applications of the method

Of course, you could also calculate on a conventional manner, in the example the zero point. But especially with functions of higher degree, whose zeros can only be determined by polynomial division, the bisection method is a good help and complement. With this technique, but you can also roots, logarithms u. Ä. approach. So you do not know even how to resolve a function or mathematical expression for an unknown, just try to determine this number by the bisection method.

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