Hey geniuses out there!
Definitely got a brain teaser here (for me anyway!).
I need some help. I'm developing some calculation software that needs to match all calculation results with an existing software (which was created by the people who created the calculation procedure for this software).
There is a lot of Linear Interpolation and I match what they get in all instances, however there is this one particular case where I can't seem to find what they're doing differently.
I'm using a very straight-forward formula which matches all instances of interpolation, except in one area, the method I'm using is:
((x - x0) × (y1 - y0) ÷ (x1 - x0)) + y0
I am then able to get the value of y.
In this one particular instance with a dataset I can't seem to find out the method they're using for interpolation to find y.
Take the following dataset for example, in brackets I've added what they represent - although not important it may help somewhat:
x (PSR) = 2.116029176481704 x0 (PSR) = 2 x1 (PSR) = 3 y0 (efficiency) = 78.6 y1 (efficiency) = 71.5 y = 77.7761928469799 = ((x - x0) × (y1 - y0) ÷ (x1 - x0)) + y0
With the above data by using standard Linear Interpolation I get 77.7761928469799, however - the method they're using gets them (to 4DP) 77.7047
There is a note against this specific case of Linear Interpolation but it's too vague for me to understand what they're doing differently.
The note says:
For the efficiency values, the interpolated efficiency is the reciprocal of linear interpolation between the reciprocals of the efficiencies.
Unfortunately I have no idea what that means in regards to how I'm to go about this Linear Interpolation any differently.
I know there are some brilliant minds on here and I hope you can help me out by giving me some insight as to how they use Linear Interpolation using that dataset to get 77.7047.
Thank you so much to anybody who helps! :)