Thread: Conditioning Number

Let f = tan x

What is the formula for the conditioning number of f? Evaluate this formula for pi/4, 1.01, 1.26 and 1.51, working to three significant figures.

Replace each of the expression for x by a 2 s.f. approximation and compute the relative error of the approximations and the functions of the approximations.

^^^^

Now, I think I can handle the calculations but I CANNOT find the formula anywhere. I don't have it in my notes and I can't find where to find it out. If someone knows this formula can you post it, I will attempt the questions.

Also, just want to check. When I evaluate the functions using the approximations to 2 s.f, would I round the result to 2 s.f too?

Do you know, at least, the definition of "conditioning number"? (I know what the "conditioning number" for a matrix or a differential equation means- but I would like to see a definition for "conditioning number" of a function.)

We are given nothing of the sort. All I know it has to do with speed of convergence and it's a formula involving dividing by x (I think). It might even be just f(x)/x. But I'm not sure and I wanted to know does anyone know this for sure.