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LEAST SQUARES APPROXIMATION Another approach to approximating a function f(x)
 

Summary: LEAST SQUARES APPROXIMATION
Another approach to approximating a function f(x)
on an interval a x b is to seek an approximation
p(x) with a small `average error' over the interval of
approximation. A convenient definition of the average
error of the approximation is given by
E(p; f)
"
1
b - a
Z b
a
[f(x) - p(x)]2 dx
#1
2
(1)
This is also called the root-mean-square-error (de-
noted subsequently by RMSE) in the approximation
of f(x) by p(x). Note first that choosing p(x) to
minimize E(p; f) is equivalent to minimizing

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences