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Quadratic least squares equation

by tza5021
Tags: equation, quadratic, squares
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tza5021
#1
Dec4-11, 04:46 PM
P: 5
f(x) = 3√x, 1 ≤ x ≤ 4
(a) Find the quadratic least squares approximating function g for the function f.

g(x)=?
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Dick
#2
Dec4-11, 06:36 PM
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The best fit function is clearly g(x)=-3/sqrt(x). But I'm guessing you trying to fit a function that's doesn't have that form. What kind of function are you trying to fit and what's the definition of 'least squares fit'?
tza5021
#3
Dec4-11, 06:47 PM
P: 5
Using g(x)= a0+a1x+a2x^2 when 1<x<4
using intergral(f(x)-g(x)dx)

tza5021
#4
Dec4-11, 06:48 PM
P: 5
Quadratic least squares equation

If you could help that would be very much appreciated as I do not knw how to punch and chug that in an intergral.
Dick
#5
Dec4-11, 06:53 PM
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Quote Quote by tza5021 View Post
If you could help that would be very much appreciated as I do not knw how to punch and chug that in an intergral.
I think you want to minimize the integral of (f(x)-g(x))^2 don't you? Put in your f(x) and your g(x). It's not a hard integral. Just square it out. It's just powers of x. Then try to minimize with respect to a0, a1 and a2.
tza5021
#6
Dec4-11, 06:55 PM
P: 5
How do I minimize the a0,a1 and a2 I do not get that part
Dick
#7
Dec4-11, 06:57 PM
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How do I minimize the a0,a1 and a2 I do not get that part
Use partial derivatives with respect to a0, a1 and a2. What should they be at a minimum? Didn't they teach you that part?
tza5021
#8
Dec4-11, 06:59 PM
P: 5
Yes, but I missed the class. So could you tell me how to do that
Dick
#9
Dec4-11, 11:40 PM
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Quote Quote by tza5021 View Post
Yes, but I missed the class. So could you tell me how to do that
What should the partial derivatives be at a minimum? Missing the class means i) you could try to find the method yourself by looking it up or reading a book or even better, ii) thinking about it yourself.


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