Assignment:
Approximate the following function f(x) = √(x + 1) 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:
Q1. Construct the divided difference table for this set of nodes and f(x).
Q2. What is Newton’s divided-difference interpolatory polynomial using all of the nodes? Use this polynomial to interpolate f(x) at x=2.25.
Q3. What is Newton’s divided-difference interpolatory polynomial using just the nodes
{1.75, 2.0, 2.5}? Use this polynomial to interpolate f(x) at x=2.25.
Newton divided difference formula:
Provide complete and step by step solution for the question and show calculations and use formulas.