Approximations and Interpolations

[pat666]

Hey,
My question is basically what is the difference between approximating and interpolating a data set?

My understanding is that interpolation must pass through every data point while approximations do not need to. Are there any other Fundamental differences?

Thanks

 

[lanedance]

"approximating" will generally assume a functional form eg. ploynomial, then choose coefficients to minimise some definition of error at known points (eg. least mean square error - LMS)

interpolating will use the closest points, and some form of function (eg. linear interpolation) to fill in the values in between the know points, by definition it will use the known values at the known points - another example of an interpolation is kriging