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November 29th, 2007, 02:13 AM   #1
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A question please

Hello to everyone, i'm a new member in the forum!

I am a greek student and i don't know the english terms for math so excuse some mistakes or difficulties to describe what i want

I have a question regarding polynomials (?).

i wonder if you can help me to create a function
i have a variety of f(x) and y and i want to make out of them the exact function

to be more precise i have these data
f(x)= 0 , y= 0
f(x)= 10 , y= 0
f(x)= 20 , y= 1
f(x)= 30 , y= 1
f(x)= 40 , y= 2
f(x)= 50 , y= 3
f(x)= 60 , y= 3
f(x)= 70 , y= 3
f(x)= 80 , y= 2
f(x)= 90 , y= 1
f(x)= 100 , y= 0
f(x)= 110 , y= -2
f(x)= 120 , y= -2
f(x)= 130 , y= -2
f(x)= 140 , y= -1
f(x)= 150 , y= -1

thanks
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November 29th, 2007, 03:23 AM   #2
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First of all, you're data is a bit weird! When you write f(x)="something" then you're already describing a function! So, I'll suppose you meant f(0)=0, f(10)=0 and so on.. Now, back to the problem! When you want to create a polynomial or that size (it will probably be a fifteen-level polynomial) it's best to use matrices. This is the way you use them:

Suppose you have a fourth level polynomial:

f(x)=a x^4+b x^3+c x^2+d x+e

then you need 5 values to be able to solve this:

f(x1)=y1
f(x2)=y2
f(x3)=y3
f(x4)=y4
f(x5)=y5

Further on, let us define two functions:

X(p)=Sum(i=1,5,(x_i)^p)
Y(p)=Sum(i=1,5,y_i*(x_i)^p)

Now we can write a matix:

|X(8) X(7) X(6) X(5) X(4)|
|X(7) X(6) X(5) X(4) X(3)|
|X(6) X(5) X(4) X(3) X(2)|=MX
|X(5) X(4) X(3) X(2) X(1)|
|X(4) X(3) X(2) X(1) X(0)|

Now, if you want to calculate the first unknown parameter (a) then just replace the first column in MX with:

|Y(4)|
|Y(3)|
|Y(2)|
|Y(1)|
|Y(0)|

And call that matrix MY. Now:

a=det(MY)/det(MX)

where det(X) denotes the determinant of X. If you want to calculate the second unknown parameter (b) then replace the second column in MX with the same column and calculate it the same way. If you wish to calculate the third, then replace the third row and so on... So, when you do this for your polynomial, you get:

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November 29th, 2007, 03:44 AM   #3
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thank you for your quick reply

and yes i did mean f(10)=0
and so on, i am a bit tired to think

and thank you for your final answer
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November 29th, 2007, 03:55 AM   #4
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Hehe... Time difference rules! You welcome!
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