2.6. Lagrange’s Interpolation Formula

Try these first

1. 1.

   What is the primary purpose of Lagrange’s Interpolation Formula?

   Hint

   Think about why we need interpolation.

2. 2.

   What type of data spacing does Lagrange’s formula work with?

   Hint

   Recall the differences from other interpolation methods.

3. 3.

   What does Lagrange's Interpolation Formula primarily deal with?

   • Equally spaced data
   • Unequally spaced data
   • Random data

   Hint

   Recall the definition of the formula.

4. 4.

   True or False: Lagrange's Interpolation Formula requires data points to be laid out in equal distances.

   • True
   • False

   Hint

   Think about what sets it apart from other methods.

5. 5.

   Given the following points: (2, 7), (3, 19), (5, 47), calculate f(4) using Lagrange’s Interpolation Formula and show your work.

   Hint

   Identify which points to use and carefully apply the Lagrange formula.

6. 6.

   Discuss the potential pitfalls of using Lagrange's method for large datasets. Provide examples.

   Hint

   Consider what happens with increased numbers of points in terms of polynomial behavior.