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# Bisection

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Calculates the zeros of a function using the bisection method.
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## Bisection

 doublebisection( double (*f)(double)[function pointer] double x0 = -1E+7 double x1 = 1E+7 double eps = 1E-10 )
The simplest root-finding algorithm is the bisection method: we start with two points a and b which bracket a root, and at every iteration we pick either the subinterval or , where is the midpoint between a and b. The algorithm always selects a subinterval which contains a root. It is guaranteed to converge to a root, however its progress is rather slow (the rate of convergence is linear).

To give you a better idea on the way this method works, the following graph shows different iterations in the approximation process. Here is the associated list of pairs chosen at consecutive steps

##### MISSING IMAGE!

This algorithm finds the roots of the user-defined function f starting with an initial interval [x0, x1] and iterating until the accuracy eps is achieved.

## References:

• F.R. Ruckdeschel, "BASIC Scientific Subroutines", Vol. II, BYTE/McGRAWW-HILL, 1981
• Wikipedia, http://en.wikipedia.org/wiki/Root-finding_algorithm

### Example 1

#include <codecogs/maths/rootfinding/bisection.h>

#include <iostream>
#include <iomanip>

// user-defined function
double f(double x) {
return (x - 2) * (x + 1) * (x + 10);
}

int main()
{
double x = Maths::RootFinding::bisection(f, -2, 0);

std::cout << "The calculated zero is X = " << std::setprecision(12) << x <<  std::endl;
std::cout << "The associated ordinate value is Y = " << f(x) << std::endl;
return 0;
}
Output:
The calculated zero is X = -1
The associated ordinate value is Y = 0

### Parameters

 f the user-defined function x0 Default value = -1E+7 x1 Default value = 1E+7 eps Default value = 1E-10

### Authors

Lucian Bentea (August 2005)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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