Module for the Newton Interpolation Polynomial
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Background. Newton Interpolation Polynomial.
Animations (Newton InterpolationPolynomial Newton InterpolationPolynomial). Internet hyperlinks to animations.
construct and evaluate the Newton polynomial
of degree that
passes through the n+1 points , for
Remark 1. Newton polynomials are created "recursively."
Remark 2. Mathematica's arrays are lists and the subscripts must start with 1 instead of 0.
Mathematica Subroutine (Newton Polynomial).
1. Form several Newton polynomials
of degree n = 1,2, 3, 4, and 5 for the
the interval using
equally spaced nodes selected from the following list
Example 2. Error Analysis. Investigate the error for the Newton polynomial approximations in Example 1.
3. What is the maximum over the
each of the quantities
3 (a). Find .
3 (b). Find .
3 (c). Find .
3 (d). Find .
3 (e). Find .
4. Application to
4 (a). Find the formula for the sum of the first n integers.
4 (b). Find the formula for the sum of the squares of the first n integers.
Old Lab Project (Newton
Interpolation Polynomial Newton
hyperlinks to an old lab project.
Research Experience for Undergraduates
Newton Interpolation Polynomial Newton Interpolation Polynomial Internet hyperlinks to web sites and a bibliography of articles.
Downloads (Newton Polynomial Newton Polynomial). Download this Mathematica notebook.
(c) John H. Mathews 2003