Quadratic extrapolation on a dataset

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Aristo
Aristo on 25 Jul 2022
Commented: William Rose on 26 Jul 2022
Is it possible to incorportate quadratic extraplotion on a 1D dataset, without using interp2 function? if so, can anybody demonstrate using a simple 1D array data.
many Thanks

Answers (1)

William Rose
William Rose on 26 Jul 2022
Yes it is possible. Three points define a quadratic equation. The quadratic equation that passes through (x1,y1), (x2,y2), and (x3,y3) is given by
This is the second order Lagrange polynomial. It is also called the Lagrange interpolating polynomial. You could also use it to extrapolate, if you wish.
  1 Comment
William Rose
William Rose on 26 Jul 2022
Here is a function that implements the Lagrange polynomial, and a script that demonstrates the use of the function. The test script does interpolation and extrapolation, to demonstrate that the quadratic polynomial passes through the three nearest points of the known data. Here is a screen shot of a typical result. The test script illustrates the fact that quadratic extrapolation is usually not a good idea.
You can also use interp1() to extrapolate - see the interp1 help.

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