# bede: Bisection Extremum Distance Estimator Method In inflection: Finds the Inflection Point of a Curve

## Description

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].

## 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 If data is concave/convex then index=1

## 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.

## 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], https://arxiv.org/pdf/1206.5478v2.pdf, 2014
[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), https://www.researchgate.net/publication/304557351, 2016

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 # ```