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# Falseposition

Calculates the zeros of a function using the Regula-Falsi method.
Controller: CodeCogs  C++

## Falseposition

 doublefalseposition( double (*f)(double)[function pointer] double x0 = -1E+7 double x1 = 1E+7 double eps = 1E-10 double maxit = 1000 )
The false position method, on contrast with Newton's method, in which the calculation of the derivative was required, replaces it with its approximation

Given and , the main algorithm is based on the following recurrence relation

This method has rate of convergence , therefore inferior to the method of Newton. However it is more accurate than Newton because only one function evaluation is required, , being calculated in the previous iteration, while Newton requires two, and .

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 the sequence above until either the accuracy eps is achieved or the maximum number of iterations maxit is exceeded.

## Example:

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

#include <iostream>
#include <iomanip>
#include <cmath>

// user-defined function
double f(double x) {
return cos(x);
}

int main()
{
double x = Maths::RootFinding::falseposition(f, 1, 3);

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 = 1.70614146372
The associated ordinate value is Y = -0.134932299622

## References:

• F.R. Ruckdeschel, "BASIC Scientific Subroutines", Vol. II, BYTE/McGRAWW-HILL, 1981

### Parameters

 f the user-defined function x0 Default value = -1E+7 x1 Default value = 1E+7 eps Default value = 1E-10 maxit Default value = 1000

### Authors

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

Source code is available when you buy a Commercial licence.

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