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Thread: Normalized Polynomial Coeffients

  1. #1
    Dec 2009

    Normalized Polynomial Coeffients

    I've been using curve fitting algorithms to derive polynomial coefficients for a given set of data. That works fine. But the problem I am having, is that the device I need to send these coefficients to says they have to be "Normalized Polynomial Coefficients". I've seen the term all over, but nowhere have even seen a definition for what that means, let alone a method for calculating it. Can someone please point me in the right direction to a link or article explaining this? Thank you in advance.
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  2. #2
    Eater of Worlds
    galactus's Avatar
    Jul 2006
    Chaneysville, PA
    I would reckon they mean something like the Legendre Polynomials.

    Say we have some vector space we can call $\displaystyle P_{2}$ and its

    inner product is $\displaystyle <p,q>=\int_{-1}^{1}p(x)q(x)dx$

    If we use the Gram-Schmidt process to to transform the standard basis,

    $\displaystyle [1,x,x^{2}]$, into an orthonormal basis.

    The polynomials in the resulting basis are called the Normalized

    Legendre Polynomials.

    Go ahead and google Legendre Polynomials and you will find plenty.

    There is an easy way to find them called Rodrigues's Formula.

    Like a unit vector, a normalized function has length 1.
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