1. ## Numerical differentiation

What is the basic principle of numerical differentiation?

2. ## Re: Numerical differentiation

What kind of derivative do you want to calculate? Do you want to for example, take some signal and find a smooth function that approximates that and take the derivative of that function?

Can you give an example of what you want to do?

3. ## Re: Numerical differentiation

This question was set in a University exam.

4. ## Re: Numerical differentiation

What topic? As it stands the question is too broad and not clear enough to know what the questioner wants.

5. ## Re: Numerical differentiation

I can't imagine what kind of answer was expected to that! My first thought was that you cannot just "do the obvious", convert the limit of $\displaystyle \frac{f(a+h)- f(a)}{h}$ to the fraction itself, with small h, because both numerator and denominator are so small "round off error" will be too large. What most numerical algorithms do is approximate f(x) by some specific kind of function, a polynomial or exponential, and take the derivative of that function. But I don't think I would call that the "basic principle".

6. ## Re: Numerical differentiation

Hi,
I would disagree a little with the previous response. Sometimes you can get away with using the difference quotient with carefully chosen h. A short discussion is found in Numerical Recipes by Press et. al. I don't have the 3rd edition, but the 2nd edition discussion starts on page 186.

7. ## Re: Numerical differentiation

It was asked in the context of Numerical analysis. The syllabus of that paper includes Newtons forward and backward interpolation formula and differentiation based on these. The question carries 2 marks.

8. ## Re: Numerical differentiation

In that case, find an interpolating function (polynomial) and get its derivative.