Constrained Hermite Taylor Series Least Squares

Like the finite difference method, the Taylor Series Least Squares method can be used to estimate derivatives. The TLS technique can be used to estimate derivatives from scattered or unstructured data. The Hermite Taylor Series Least Squares technique augments the TLS approach with information about the derivative of the function. The Constrained Hermite Taylor Series Least Squares technique augments the HTLS technique by constraining the least squares problem to match the derivative at the point of interest.

This method is fully developed in:

McDonald, Robert A. and Ramos, Alejandro, 'Constrained Hermite Interpolation for Mesh-Free Derivative Estimation Near and On Boundaries', AIAA Journal, October 2011 vol. 49 no. 10, pp. 2248-2257. DOI: 10.2514/1.J051042