# Polynomial and Rational Function Modeling - Rational Function Models - Advantages

Rational function models have the following advantages:

1. Rational function models have a moderately simple form.
2. Rational function models are a closed family. As with polynomial models, this means that rational function models are not dependent on the underlying metric.
3. Rational function models can take on an extremely wide range of shapes, accommodating a much wider range of shapes than does the polynomial family.
4. Rational function models have better interpolatory properties than polynomial models. Rational functions are typically smoother and less oscillatory than polynomial models.
5. Rational functions have excellent extrapolatory powers. Rational functions can typically be tailored to model the function not only within the domain of the data, but also so as to be in agreement with theoretical/asymptotic behavior outside the domain of interest.
6. Rational function models have excellent asymptotic properties. Rational functions can be either finite or infinite for finite values, or finite or infinite for infinite x values. Thus, rational functions can easily be incorporated into a rational function model.
7. Rational function models can often be used to model complicated structure with a fairly low degree in both the numerator and denominator. This in turn means that fewer coefficients will be required compared to the polynomial model.
8. Rational function models are moderately easy to handle computationally. Although they are nonlinear models, rational function models are particularly easy nonlinear models to fit.

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