2
$\begingroup$

I came across this question:

Suppose $f(x)=x^3-x+\frac{1}{4}$, What's the value of $f [0,0.1,0.2,0.3,0.4]$?

The problem is, I have no idea what is being asked, I'm unfamiliar with the notation "$f[0,0.1,0.2,0.3,0.4]$".

  • 0
    @Gigili: what Gerry is telling you here is that you should have mentioned the book/paper/whatever where you saw this notation. This is explicitly requested in the popup for the [tag:notation] tag, among other things.2012-02-14

2 Answers 2

7

This notation is used for divided differences, so perhaps that is what you are being asked to calculate. Giving a context for the question would help: divided differences arise in polynomial interpolation.

  • 0
    @Gigili: entirely your call. But I deliberately left gaps in reasoning in my comment that you have to fill, should you decide to post an answer.2012-02-14
2

As user12477 pointed out, it's Newton's divided differences interpolation polynomial and as J.M. pointed out, while $f(x)$ is a cubic function (polynomial of degree $n=3$), the divided difference on $n+1=4$ points (more than $n$ points generally) is equal to zero.