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Newton Divided Difference Interpolatory Polynomial

Author:
October 4th, 2022

Hi,
Your assistance with the following interpolation problem would be appreciated. I do have an existing Maple program that might be of assistance. Please let me know if you would like it.
Approximate the following function using the set of nodes
{1.0, 1.25, 1.75, 2.0, 2.5, 3.0}
Use the Newton divided – difference interpolatory polynomial to:
1. Construct the divided difference table for this set of nodes and
2. What is Newton’s divided-difference interpolatory polynomial using all of the nodes? Use this polynomial to interpolate at x=2.25.
3. What is Newton’s divided-difference interpolatory polynomial using just the nodes
{1.75, 2.0, 2.5}? Use this polynomial to interpolate at x=2.25.

Newton divided difference formula:

See: Numerical Analysis, Burden & Faires p. 121

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