Question

I know how to find finite differences such as first or second differences. But what if the x co-ordinates given are in random order.

Answer 1

I don't even know what it means...much less how to solve it.

Answer 2

For example

x y
1 3
3 -3
4 -9
2 1

Answer 3

When I find the first differences for the first y consecutive y values or even the second consecutive y values, I will not know if its first or secind differences because the x vaules are random and are not increasing by the same amount, what do I do in this case

Answer 4

does tis make sense @Mertsj

Answer 5

Newton's method of finite differences won't work if the \(x\)'s aren't equally spaced apart.

Answer 6

There is a way but I do not recall...

Answer 7

1) Sort them. Why is that hard?
2) Points not equally spaced simply requires a different denominator.

0 1
1 5
3 9

Unit Differences are (5-1)/(1-0) and (9-5)/(3-1)

Answer 8

Yes but this was a simple example, what if they were not sortable?

Answer 9

I want to how how to find wether they are first or second differences without sorting them because realistically, we cannot always sort them

Answer 10

ill say it again, As I have said this @tkhunny guy/ girl is good

Answer 11

Ummm... Real Numbers are Well-Ordered. Why are the not sortable? Realistically, we can always sort them.

Answer 12

Ok, say the pattern was

1 2
3 6
4 12
7 18

How can we sort this, and find if they are first or second differences

Answer 13

I suppose we could have precision problems so that we can't actually tell if they are sorted.

I suppose, if they cannot be sorted, that we can still index them. This would be essentially "sorted".

Oh, how I wish I understood the question. What are these?

1 2
3 6
4 12
7 18

Are you saying these are NOT abscissas and ordinates? We believe these to be differences of some kind?

Answer 14

These are co-ordinates the first are x and second are y

Answer 15

Okay, how are they not sorted?

Answer 16

we are missing x values of 2 5 and 6..

Answer 17

Well, that seems to have nothing to do with sorting. They are just not evenly-spaced. This is where I started this conversation. You must unitize the differences.

1 2
3 6
4 12
7 18

Available 1st Differences
(6-2)/(3-1) = 4/2 = 2
(12-6)/(4-3) = 6/1 = 6
(7-4)/(18-12) = 3/6 = 1/2

Available 2nd Differences
(6-2)/(4-1) = 4/3
((1/2)-6)/(7-4) = (-11/2)/3 = -11/6

These are not quite the Unit Differences you are used to. They are more of an average over the provided range.

Answer 18

Wow, but would that would for

x y
1 3
3 -3
4 -9
2 1

Answer 19

You can see these date from y = x^3, one with complete data and the other with some values missing.

1 1
2 8 7
3 27 19 12
4 64 37 18 6
5 125 61 24 6
6 216 91 30 6
7 343 127 36 6

1 1
3 27 13
4 64 37 8
7 343 93 14 1

It's not as good as one might want, but it's more than nothing.

Answer 20

http://en.wikipedia.org/wiki/Divided_differences