Introduction
The data is of the form
(0.1)
fi  f A  xi ; c    i   Sys
The expectation value of fi – fA over an ensemble of evaluation is Sys owing to the
random nature + and – of the i. The expectation value of the square of this is
f
i
 f A  xi ; c  
2
2
2
  i2  2 i  Sys   Sys
  2  x; c    Sys
 x
(0.2)
Finding the error coefficients
The error coefficients here are assumed to be of the form
 m

(1.1)
 2  f A  xi ; c    max   cJ f AJ 1 ,  min 
 J 1

When fA is positive definite and only c2 is greater than zero the errors have a
Poisson distribution. When only c3 is greater than 0 the errors are given by cerr  |f| so
that 100cerr is the percentage error. The term min is added to the polynomial to make
(1.1) positive definite.
The error coefficients can be found by minimizing
N
2
2
  aerr , berr , cerr ,  min     fi  f A  xi     2  f A  xi  ; aerr , berr , cerr ,  min  (1.2)


i 1
This is another polynomial. Nlfit needs to output
x =| fA(xi)| function = (fi-fA(xi))2
f
Function
2
Polerr
The approximating function (1.1) is a simple polynomial when it is greater than min, it is
min with zero derivatives otherwise. The value of min is passed to the poly routine as the
last constant in PolErr.for.