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How hard is it to invert? e.g. given a set of points along a particular curve, how difficult is it to find the values of the 6 parameters that generated it?
by arcanus 10y ago
How hard is it to invert? e.g. given a set of points along a particular curve, how difficult is it to find the values of the 6 parameters that generated it?
- vinchuco 10y agoIf you know a,b,m,n1,n2,n3, and use sufficient points, you may be able to get an interpolated approximation. In general, one can fit many such curves through a finite set of points. http://math.stackexchange.com/questions/65970/can-a-function-be-found-to-fit-any-set-of-points http://math.stackexchange.com/questions/65970/can-a-function... A question originally asked by Leibniz to determine the measure of usefulness of a law. https://plus.maths.org/content/omega-and-why-maths-has-no-toes https://plus.maths.org/content/omega-and-why-maths-has-no-to.... If you don't have the 6 parameters, good luck. A unique inverse is defined only for injective functions.
- mturmon 10y agoSomeone experimented with this. See the links at the bottom of the Wikipedia article. This seems misguided to me -- why use a curve family when fitting is so hard -- but it has been done.