Polynomial and Rational Function Modeling - Rational Function Models

Rational Function Models

A rational function is simply the ratio of two polynomial functions.

y = \frac{a_{n}x^{n} + a_{n-1}x^{n-1} + \ldots + a_{2}x^{2} + a_{1}x + a_{0}} {b_{m}x^{m} + b_{m-1}x^{m-1} + \ldots + b_{2}x^{2} + b_{1}x + b_{0}}

with n denoting a non-negative integer that defines the degree of the numerator and m is a non-negative integer that defines the degree of the denominator. For fitting rational function models, the constant term in the denominator is usually set to 1. Rational functions are typically identified by the degrees of the numerator and denominator. For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. A rational function model is a generalization of the polynomial model: rational function models contain polynomial models as a subset (i.e., the case when the denominator is a constant).

Read more about this topic:  Polynomial And Rational Function Modeling

Famous quotes containing the words rational, function and/or models:

    “After I went to bed I had a curious fancy as to dreams. In sleep the doors of the mind are shut, and thoughts come jumping in at the windows. They tumble headlong, and therefore are so disorderly and strange. Sometimes they are stout and light on their feet, and then they are rational dreams.”
    —James Boswell (1740–1795)

    “We are thus able to distinguish thinking as the function which is to a large extent linguistic.”
    —Benjamin Lee Whorf (1897–1934)

    “Grandparents can be role models about areas that may not be significant to young children directly but that can teach them about patience and courage when we are ill, or handicapped by problems of aging. Our attitudes toward retirement, marriage, recreation, even our feelings about death and dying may make much more of an impression than we realize.”
    —Eda Le Shan (20th century)