Description Usage Arguments Details Value Author(s) References See Also Examples

It iterates in a way similar to the well known bisection method in root finding, with the only exception 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].

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

`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 |

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

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. |

Demetris T. Christopoulos

[1]Demetris T. Christopoulos (2014). Developing methods for identifying the inflection point of a convex/concave curve. arXiv:1206.5478v2 [math.NA]. https://arxiv.org/pdf/1206.5478v2.pdf

[2]Demetris T. Christopoulos (2016). On the efficient identification of an inflection point.International Journal of Mathematics and Scientific Computing, (ISSN: 2231-5330), vol. 6(1). https://veltech.edu.in/wp-content/uploads/2016/04/Paper-04-2016.pdf

See also the simple version `ede`

, `edeci`

and iterations plot using `findipiterplot`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
#
#Fisher-pry model with heavy noise, unequal spaces
#and 1 million cases:
N=10^6+1;
set.seed(2017-05-11);x=sort(runif(N,0,10));y=5+5*tanh(x-5)+runif(N,-1,1);
#
ptm <- proc.time()
tede=ede(x,y,0);tede;proc.time() - ptm
# j1 j2 chi
# EDE 351061 648080 4.997139
# user system elapsed
# 0.02 0.02 0.05
#
``` |

```
j1 j2 chi
EDE 351061 648080 4.997139
user system elapsed
0.029 0.000 0.030
```

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