Find an equation from more than 2 coordinate point

[sit06603_wesley]

Find an equation from more than 2 coordinate point

[Question]
if I have a list of coordinate... let say...
(2, 17)
(3, 25)
(4, 19)
(5, -1)
can u find an equation which can suit all the coordinate above...???
(I suppose... it also will work for more than this number coordinate,
it can be five or more)....
Hopefully there is some one that can help me...!!!

May be I change another way

let say:
x-2y=17 (2, 17)
x-3y=25 (3, 25)
x-4y=19 (4, 19)
x-5y=-1 (5, -1)

Is what my Idea loh... previously I just give a list of
coordinate... and require to produce or figure out an
equation which able to solve the problem... where...
when I....

-> insert 2 in to that equation.... it able to output 17 as
a result....
-> insert 3 in to that equation.... it able to output 25 as
a result....
-> insert 4 in to that equation.... it able to output 19 as
a result....
-> insert 5 in to that equation.... it able to output -1 as
a result....

is that POSSIBLE...??? [ Hopefully is possible].....
plz..... is urgent.... S.O.S~......


An Idea.... just an Idea.....
Now... I assume there is a equation for each coordinate....
where it is in the form of....

-> x-Ay=B (A, B)
-> where, A={0, 1, 2, 3..... n}, and B is the result.....

:. If there is a possible to solve x, y from that list of
equation.... there might be possible.... or any one got
better idea...

plz.... help me..... S.O.S.... is urgent to solve some
problem...... 0_o???

"Plz reply me as soon as possible....." S.O.S~......




Trully,
Wesley
[sit06603@rediff.com]

[Matt Gregory]

You're on the wrong forum. Go Google for "Babbage's Method".

[DHodges]

is that POSSIBLE...??? [ Hopefully is possible].....
plz..... is urgent.... S.O.S~......

Yes, it is possible. Given N points, it is possible to fit a polynomial of at least degree N-1. (That's probably the most parsimonious solution that is is continuous.)

But it occurs to me just now that it could be also be done in a method like Fourier analysis, with a function defined as a sum of sines and cosines. Since you have a small number of points, this would likely be a finite sum.

It's possible that the sum of sines and cosines could be considered more parsimonious than the polynomial, but I don't see how you can decide that without actually fitting both to the given points, and then the parsimony is a matter of opinion, really.

If you don't require a continuous function, then there is a trivial solution, as you pretty much spelled out. If it needs to be continuous, but not first-derivative continuous, then you can construct a series of line segments, meeting at the given points.

A first-derivative continuous solution can be constructed using cubic splines. For many applications, that would be a good solution, especially if you have a larger number of points.


Now, go do your damn homework.