Aitken’s Graphical Construction for Lagrange Interpolation

I first became aware of Aitken’s Graphical Construction of Lagrange Parabolic interpolation from an article that appeared in the Design News Magazine.

The article presented a graphical construction for the generation of points on a parabola. The significant feature was that the construction presented a method for generating exact point on the parabola. And it pointed out that the construction was an analog for the Lagrange Three Point Polynomial.

Citation for the Design News Reprint

Citation for the Design News Reprint

The Authors of the Design News Article

The Authors of the Design News Article

The original three point construction

The original three point construction

I was able to rework their construction into a more useful form and I also created a FORTRAN statement function which I then used to reproduce the construction.

My three point Construction and FORTRAN Code

My three point Construction and FORTRAN Code

And here is more detail about the FORTRAN FLINE Statement function.

Details for the FLINE function

Details for the FLINE function

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