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# Bisection

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Calculates the zeros of a function using the bisection method.
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Contents

C++

## 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

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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