Name of convergence method

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Jakob Sievers
Jakob Sievers on 16 Dec 2013
Commented: Jakob Sievers on 16 Dec 2013
Hi all
This is strictly speaking not a Matlab question, but it does refer to a method I am applying in Matlab and I am unsure of where else to post it. I have a series of numbers for which I can test each individually against an elaborate set of functions and get a binary response (i.e.: accepted or denied). I am interested in finding the last number for which the response is "accepted". Rather than running all individual numbers (which would be very time-consuming) I run the first and the last number (boundaries) and then a middle-point while iteratively shifting the boundaries, and thus the middle point, based on the output response. The boundaries approach one another quickly and convergence of the middle point is usually ensured within ~10-15 iterations despite a very large range of possible input numbers. The approach is somewhat similar to the Newton-raphson method though involving repeated halving of the area being examined rather than using line trends.
My problem is this: This method has undoubtedly been invented ages ago, but I don't know what it is called or who developed it. It just seemed like a clever way to solve the problem but now that I have to describe as part of a paper I am working on I'd like to know what it is called rather than saying "similar to Newton-Raphson".
Can anyone help me?
Jakob Denmark

Accepted Answer

Matt J
Matt J on 16 Dec 2013
Edited: Matt J on 16 Dec 2013
Bisection? Compare to
and see if it's what you mean.

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