show/hide this revision's text 3 Clarified (see the comments)

I have a (one dimensional) set (I will name it S)S of real numbers, and I would like to create a new set (I will name it R) with exactly n points real numbers (not necessarily from the set) that represent it best.

What I mean by best?

Well, I have query that asks for given point what is the closest point from S to that point, and when I ask same thing for set R I would like to have best fit to the real answers.

To be specific, how do I minimize the Hausdoff distance between S and R?

I hope I've been clear enough in what i want. I've heard of mathoverflow, so I said to myself why wouldn't I ask for help there.

Thank you in advance.

(Edited in light of the comments below.)
show/hide this revision's text 2 Fixed title

Aproximating Approximating a set with fixed number of elements

I have a (one dimensional) set(I set (I will name it S), and I would like to create a new set(I set (I will name it R) with exactly n points (not necessarily from the set) that represent it best.

What I mean by best?

Well, I have query that asks for given point what is the closest point from S to that point, and when I ask same thing for set R I would like to have best fit to the real answers.

I hope I've been clear enough in what i want. I've heard of mathoverflow, so I said to myself why wouldn't I ask for help there.

Thank you in advance.
show/hide this revision's text 1

Aproximating a set with fixed number of elements

I have a (one dimensional) set(I will name it S), and I would like to create a new set(I will name it R) with exactly n points (not necessarily from the set) that represent it best.

What I mean by best?

Well, I have query that asks for given point what is the closest point from S to that point, and when I ask same thing for set R I would like to have best fit to the real answers.

I hope I've been clear enough in what i want. I've heard of mathoverflow, so I said to myself why wouldn't I ask for help there.

Thank you in advance.