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I would like to recreate a function only by knowing points on the graph.

So I would have the points

A(x/y) B(x/y) C(x/y)

and would like to create its f()

Is this possible?

I heard this should be possible with a Taylor Series but to do a Taylor Series wouldn't I need a f() and its derivative in the first place?

Jason
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  • Sure. You could just make it linear between points where it is defined. If you want smoothness, one common approach is spline functions: http://en.wikipedia.org/wiki/Spline_%28mathematics%29 – Thomas Andrews Jul 22 '13 at 15:57

1 Answers1

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A common method for determining a function which runs through some number of points is Lagrange interpolation. There are explicit formulas you can look up (Hoffman and Kunz linear algebra textbook, or look it up on Wikipedia/MathWorld) which help you construct a polynomial function which has intersection points with the desired ones you plugged into the formula. Keep in mind that there need not be a unique continuous function which runs through a given set of points in the plane and that there are a variety of interpolation techniques. You can also use the Stone-Weierstrass theorem to construct a polynomial function in a similar way, but this is a bit harder to understand, Lagrange interpolation is probably what you are looking for.

Reference: Lagrange Interpolation on Wolfram MathWorld

Samuel Reid
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  • Just glanced over the Mathworld article and it looks like what I am looking for. Thanks – Jason Jul 22 '13 at 16:03