Chord method is used for finding root of the function in given interval.

## Algorithm:

IN: Function f, which is continous function and interval [a,b]. Function must satisfy given equation: f(a) * f(b) < 0 - signs of that values are different, which means that given function in given interval has at least one root in interval [a,b]. OUT: Root in given interval. 1. Calculate x = (a * f(b) - b* f(a)) / (f(b) - f(a)); 2. Check if abs(f(x)) < precision. 3. If it is end algorithm and return x. 4. Check if f(a) * f(x) < 0. 5. If it is make x = (x * f(a) - a* f(x)) / (f(a) - f(x)). 6. Else make x = (x * f(b) - b * f(x)) / (f(b) - f(x)). 7. Go to step 2.

## Sample Output:

f(x) = x * (x + 2) -1 [-3, 0] root: -2.414201183431953

## Chord Method Step By Step

Iteration Number | a | b | x | f(xn) |
---|---|---|---|---|

1 | -3 | 0 | -1 | -2 |

2 | -3 | 0 | -2 | -1 |

3 | -3 | 0 | -2.3333333333333335 | -0.22222222222222188 |

4 | -3 | 0 | -2.4 | -0.04000000000000026 |

5 | -3 | 0 | -2.4117647058823533 | -0.006920415224912602 |

6 | -3 | 0 | -2.413793103448276 | -0.0011890606420928984 |

7 | -3 | 0 | -2.4141414141414144 | -2.0406081012080968E-4 |

8 | -3 | 0 | -2.414201183431953 | -3.501277966366789E-5 |

## Pros:

- easy to implement.
- faster than bisection method.
- no need to calculate derivative of given function.

## Cons:

- has trouble with some functions.

Chord Method Algorithm