Description

Hermite interpolation
1. In the following table there are some data regarding a moving car. UseHermite interpolation to estimate position and speed of the car when the time is t = 10.
Time 0 3 5 8 13
Distance 0 225 383 623 993
Speed 75 77 80 74 72
2. Plot, in the same gure, the graphs of the function f : [ 5;5] ! R; f(x) = sin2x and of the corresponding Hermite interpolation polynomial, considering 15 equidistant nodes in [ 5;5].
Facultative:
3. The data from the following table are generated using the function f(x) = xlnx :
x f(x) f0(x)
8:3 17:56492 3:116256
8:6 18:50515 3:151762
Use the Hermite interpolation polynomial to approximate f(8:4) and nd the absolute error.
4. Let f(x) = 3xex e2x:
a) Approximate f(1:03) by the Hermite interpolation polynomial of degree
at most three, using x0 = 1 and x1 = 1:05 and nd the absolute error.
b) Repeat (a) with the Hermite interpolation polynomial of degree at most
ve, using x0 = 1 and x1 = 1:05 and x2 = 1:07 and nd the absolute error.
c) Plot the graphs of the function f and of the interpolation polynomials from (a) and (b).
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