Error margins

[born2laser]

(10-28-2024 05:47 PM)carey Wrote:  The issue with calculating derivatives numerically is that the process of numerical differentiation (taking a difference divided by a difference) dramatically increases noise (i.e., error).

You are absolutely right in what you say, in particular if you are trying to calculate the derivative of a function with added fluctuations, but that is not what I meant. To propagate error you need to take the derivative of the formula used to calculate the value based on the parameters, instead of putting pen to paper to work out the partial derivatives I just programmed that function as an RPN program and had a program that then approximated the derivative with a numerical method (evaluating the function at the point of interest and varying the value of one parameter at a time). It is good for any function and involves approximating the function locally with a polynomial of any desired degree, it is most definitely not good for experimental data with noise, but good for mathematical functions. I used degree=3, which is overkill, but in my defense I have to say I was reading a book on numerical methods at the time and had a 41 in my hands!