2.5. Central Difference Interpolation Formulas

Try these first

1. 1.

   Define central difference interpolation.

   Hint

   What does it mean to look both ways in interpolation?

2. 2.

   What is Stirling's Formula used for?

   Hint

   Think about where you would place a midpoint.

3. 3.

   What does Central Difference Interpolation rely on to estimate a function's value?

   • Forward differences
   • Evenly spaced points
   • Surrounding data points

   Hint

   Think about where the estimation gets its influences.

4. 4.

   True or false: Stirling's Formula is used for points near the beginning of a dataset.

   • True
   • False

   Hint

   Where does Stirling prefer to work?

5. 5.

   Given data points (1, f(1)), (2, f(2)), (3, f(3)), and (4, f(4)), use Stirling's formula to estimate f(2.5) if f(1), f(2), f(3), and f(4) are known.

   Hint

   Identify the differences in y-values first.

6. 6.

   Analyze a set of five data points and determine the best way to interpolate a value close to the middle using both Stirling's and Bessel’s formulas. Discuss their outcomes.

   Hint

   How do the results differ based on placements?