2.1. Interpolation Basics

Try these first

1. 1.

   Define interpolation in your own words.

   Hint

   Think about how you would predict a temperature for a day not directly measured.

2. 2.

   What is a forward difference?

   Hint

   Use the formula Δy = y(i+1) - y(i) for clarity.

3. 3.

   What is interpolation primarily used for?

   • Estimating unknown values
   • Finding maximum values
   • Deriving equations

   Hint

   Think about the gaps between data points.

4. 4.

   True or False: Interpolation can be used for equally and unequally spaced data.

   • True
   • False

   Hint

   Consider all methods discussed.

5. 5.

   Using the points (1, 1), (2, 4), (3, 9), estimate f(2.5) using Lagrange's interpolation.

   Hint

   Think of how you'd construct the Lagrange polynomial using the three points.

6. 6.

   Given equally spaced data points (0, 1), (1, 1.5), (2, 2), estimate f(1.5) using Newton's forward method.

   Hint

   Calculate forward differences first to use them effectively.