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Dear all,

I would like to get coefficient C0, C1....CN from the below equation,

I have enclosed herewith an excel having x and y co-ordinates.

Can anybody please let me know how to write this equation in 'custom equation' option in curve fitting tool or is there any other way to do it?

Catalytic
on 27 Jul 2019

C = polyfit( sqrt( x.^2+y.^2) , Z, N)

Matt J
on 28 Jul 2019

It's not that polyfit is better or worse at fitting high order polynomials. It's just that high order polynomials are typically a bad thing to use as a model due to numerical instability.

For example the relationship between a polynomial's roots and its coefficients gets unstable at orders higher than about 20, as illustrated below. Notice the errors just in recovering the roots from the coefficients - I haven't even done any curve fitting yet.

>> p=poly(1:20); r=real(roots(p))

r =

19.9999

19.0013

17.9937

17.0185

15.9597

15.0593

13.9302

13.0627

11.9589

11.0225

9.9912

9.0027

7.9994

7.0001

6.0000

5.0000

4.0000

3.0000

2.0000

1.0000

Matt J
on 29 Jul 2019

As you mentioned as its a higher order polynomial I will not use polyfit due to higher perecentage error.

No, that is not what I said. What I said was "It's not that polyfit is better or worse at fitting high order polynomials. It's just that high order polynomials are typically a bad thing...".

Stop using high order polynomials. Use splines instead.

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