2.7. Newton’s Divided Difference Formula

Try these first

1. 1.

   What is the definition of a divided difference?

   Hint

   Think about how you calculate the changes in y values.

2. 2.

   What is the first term in Newton's interpolation formula?

   Hint

   It’s always the initial value of f.

3. 3.

   What is the first divided difference for points (1,2) and (2,4)?

   • 1
   • 2
   • 3

   Hint

   Focus on the formula for divided differences.

4. 4.

   True or False: Divided differences can only be calculated if data points are evenly spaced.

   • True
   • False

   Hint

   Think about the flexibility of this method.

5. 5.

   Given the points (0, 1), (1, 3), (2, 2), (3, 5), derive the polynomial using Newton's Divided Differences and find the value at x=1.5.

   Hint

   Make sure to carefully calculate each section of your divided difference table.

6. 6.

   You have data points (2, 4), (3, 1), (5, 3). Create a Newton's divided difference table and find f(4).

   Hint

   Watch out for negative differences that can affect your calculations!