Bisection Extremum Distance Estimator Method
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 , .
bede(x, y, index)
The numeric vector of x-abscissas, must be of length at least 4.
The numeric vector of the noisy or not y-ordinates, must be of length at least 4.
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:
the last EDE estimation that was found
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.
New function in version 1.2
Demetris T. Christopoulos
Demetris T. Christopoulos, Developing methods for identifying the inflection point of a convex/ concave curve, arXiv:1206.5478v2 [math.NA], 2012.
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 the simple version
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