2.4. Newton’s Backward Interpolation Formula

Try these first

1. 1.

   What is the formula for Newton's Backward Interpolation?

   Hint

   Look for the structure of the interpolation formula in your notes.

2. 2.

   Define finite differences.

   Hint

   Think about how we approximate derivatives.

3. 3.

   What does u represent in Newton's backward interpolation formula?

   • The next y value
   • The last known y value
   • The relative position of x

   Hint

   Think about how u connects to the values of x.

4. 4.

   True or False: Newton's Backward Interpolation is suited for estimating values near the start of a dataset.

   • True
   • False

   Hint

   Recall the specific application of this formula.

5. 5.

   With known data points (1, 2), (2, 6), and (4, 24), estimate f(3) using the backward interpolation formula. Show your calculations for each step.

   Hint

   Make sure to verify the backward differences used.

6. 6.

   Given data points of y-values at (1, 1), (2, 4), (3, 9), (4, 16), use backward interpolation to find f(3.5). Display all workings.

   Hint

   Take your time to check the step size and differences defined.