# Bisection Extremum Distance Estimator Method

### Description

It iterates in a way similar to the well known bisection method in root finding, with the only exception is that
our *[a_n,b_n]* intervals contain the inflection point now and the rule for choosing them follows definitions
and Lemmas of [1], [2].

### Usage

1 | ```
bede(x, y, index)
``` |

### Arguments

`x` |
The numeric vector of x-abscissas, must be of length at least 4. |

`y` |
The numeric vector of the noisy or not y-ordinates, must be of length at least 4. |

`index` |
If data is convex/concave then index=0 |

### Details

It is the fastest solution for very large data sets, over one million rows.

### Value

It returns a list of two elements:

`iplast` |
the last EDE estimation that was found |

`iters` |
a matrix with 4 columns ("n", "a", "b", "EDE") that give the number of x-y pairs used at each iteration, the [a,b] range where we searched and the EDE estimated inflection point. |

### Note

New function in version 1.2

### Author(s)

Demetris T. Christopoulos

### References

[1]Demetris T. Christopoulos, Developing methods for identifying the inflection point of a convex/ concave curve, arXiv:1206.5478v2 [math.NA], 2012.

[2]Demetris T. Christopoulos, On the efficient identification of an inflection point,International Journal of Mathematics and Scientific Computing,(ISSN: 2231-5330), vol. 6(1), 2016.

### See Also

See also the simple version `ede`

.

### Examples

1 2 3 4 5 6 7 8 |