Chapter 7: Interpolation Topics

Topics and Sections from the Text:

Questions and Exercises From Chapter 7

Review Questions: pages 333-335, #7.1, 7.3 - 7.5, 7.10, 7.12, 7.13, 7.15 - 7.21, 7.23, 7.24, 7.27 - 7.29

Exercises: pages 335-336, #7.1 - 7.5, 7.15

Additional Exercises

  1. Do there exist a, b, c, and d so that the following function is a natural cubic spline?
                         -x                   for  x in [-10, -1]
          S(x) =      ax^3 + bx^2 + cx + d    for x in [-1, 1]
                          x                   for x in [1, 10]
    

  2. List all the ways in which the following fails to be a natural cubic spline.
                        x + 1             for x in [-2, -1]
          S(x) =     x^3 - 2x + 1         for x in [-1, 1]
                        x - 1             for x in [1, 2]
    

  3. Given the data points (-1, 3), (1, 5), (2, 1). Write the equations one would need to solve to interpolate these points with
    (a) A quadratic spline
    (b) A natural cubic spline