How the Toolkit came to be.
First realization
- I want my mathematics to be intuitive.
- I want to see it.
- I want to understand it.
- I want to own it.
Second realization
- When applying curve fitting to physical data, knowing the theoretical behaviors does not make the error terms in the curve fit any smaller than if you did not know the theoretical behavior.
- This then led me to focus the local behavior of a curve.
- Focusing on three points at a time while sliding over the extent of the curve.
Third realization
- stacking the deck to facilitate the desired outcome is right and proper attitude for practical numerical techniques.
Fourth realization
- Statement Functions in FORTRAN are cool.
The three seeds that formed the foundation of the Toolkit:
- A paper on Aitken’s Graphical Analog for Constructing Lagrange Polynomials
- A drafting textbook describing how a carpenter can measure arc length
- While reading textbooks on numerical analysis – there are always long glowing chapters on integration touting how averaging is the key to good results. While the very next chapter on differentiation is short and the author always advises the reader not to get involved. This led me to consider the possibility of incorporating an averaging technique into a process for numerical differentiation.