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Math Help - Finite Differences

  1. #1
    Junior Member masoug's Avatar
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    Question Finite Differences

    Hi,
    I am in an Algebra II course where we talk about function fitting with polynomials. We use a method called finite differences to find the degree polynomial that fits the given data (x and y values).

    What makes finite differences tick? Why does it work?

    Thanks!

    -Masoug
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by masoug View Post
    Hi,
    I am in an Algebra II course where we talk about function fitting with polynomials. We use a method called finite differences to find the degree polynomial that fits the given data (x and y values).

    What makes finite differences tick? Why does it work?

    Thanks!

    -Masoug
    What makes it work is that the differences of a polynomial of degree n are the values of a polynomial of degree n-1, so if you keep taking the differences of differences you get polynomials of decreasing degree, eventually arriving at a polynomial of degree 0 which is a constant. The number of differences you need to take to arrive at a constant is the degree of the original polynomial.

    CB
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