Interpolation and Curve Fitting

Curve Fitting
• Given m data points (x i , y i ), find n-vector a of
parameters that gives “best fit”to model
function y = f(x, a), m
2
min ( y f
( x,
a))
• Problem is linear if function f is linear in
components of a
f ( x,
a)
a
(
x)
a
(
x)
a
n(
x)
1 1 2 2
n
Aa≈b with A ij =φ j (x i ) and b i =y i
i1
• Problem can be written in matrix form as
a
i
Numerical Methods © Wen-Chieh Lin 37