How does the 'cubic' method for griddedInterpolant work?

I would like more more information on the algorithm behind the 'cubic' interpolation used in the 'griddedInterpolant' function. I would also like to know whether it's possible to supply my own gradients to the function?

Answer 1

[MathWorks Support Team]

The ‘cubic’ method in 'griddedInterpolant' is the same as ‘v5cubic’ in 'interp1':

https://www.mathworks.com/help/matlab/ref/double.interp1.html?#inputarg_method

In addition to this documentation, there is a brief explanation of 'v5cubic' on Cleve's blog (under 'Interp1'):

https://blogs.mathworks.com/cleve/2012/07/16/splines-and-pchips/

The 'cubic' method of 'griddedInterpolant' is a local C1 piecewise cubic Hermite interpolation method where the slope at a grid point x(n) is the mean of neighboring values y(n-1) and y(n+1).

This method does not support user-defined derivatives and requires the abscissa x to be equally spaced.