1.1.6. Newton’s Forward and Backward Interpolation Formulas

Try these first

1. 1.

   What is the forward interpolation formula?

   Hint

   Recall the components of the formula from our discussion.

2. 2.

   Define finite difference.

   Hint

   Think about how differences in values help in approximating derivatives.

3. 3.

   What does the forward interpolation formula estimate?

   • Value at existing data point
   • Value between data points
   • Value outside the dataset

   Hint

   Think of how we fill in gaps in data.

4. 4.

   True or False: The backward interpolation formula can only estimate values after the last known point.

   • True
   • False

   Hint

   Consider what backward means in this context.

5. 5.

   Given the data points (1, 1), (2, 4), (3, 9), and (4, 16), calculate f(2.5) using the forward interpolation formula.

   Hint

   Set up your forward difference table to help track your computations.

6. 6.

   Using the same data points, estimate f(3.5) with the backward interpolation formula. Discuss your reasoning.

   Hint

   Remember that you are predicting backward, so focus on the point at 3.