COnnecting the dots... The art and science of interpolation and extrapolation

The COMMUNITY MATHEMATICS CENTRE, COMAC (2017) COnnecting the dots... The art and science of interpolation and extrapolation. At Right Angles, 6 (2). pp. 12-16.

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Abstract

he following is an extremely common scenario in the sciences: two variables y and x are connected by a functional relation, y = f(x), but f is unknown and our task is to find it. The only actions available to us are to perform experiments and find the values of y corresponding to selected values of x. After doing these experiments, we obtain the following n pairs of values of x and y: M α C er and compass is part of the standard geometry syllabus at the is a standard procedure for doing We the may job, is so plot and these it points on a simple sheet of graph paper and get something which like this: if not t to think of an alternative to it that is just as looks simple, procedure, announced in a Twitter post [1]. A F Figure 1 D Angle bisector Armed with only these data points, can we determine the unknown function f? Another way of expressing this question is the following: Can we fit a definite, unique curve to these data points? Note that the curve must pass through all the points. (So this is not a problem of finding the “line of best fit” or the “curve of best fit”). I A moment's reflection will tell us that the answer is No. The question is too broad to admit an answer when stated this way. Even if we were only interested in polynomial functions f (this is very often the case), it is still not possible for the data to yield

Item Type: Articles in APF Magazines
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University publications > At Right Angles
Depositing User: Mr. Sachin Tirlapur
Date Deposited: 15 Sep 2018 09:45
Last Modified: 15 Sep 2018 09:45
URI: http://publications.azimpremjifoundation.org/id/eprint/1335
Publisher URL: http://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-...

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