Summary: PIECEWISE POLYNOMIAL INTERPOLATION
Recall the examples of higher degree polynomial in-
terpolation of the function f(x) =
1 + x2
[-5, 5]. The interpolants Pn(x) oscillated a great
deal, whereas the function f(x) was nonoscillatory.
To obtain interpolants that are better behaved, we
look at other forms of interpolating functions.
Consider the data
x 0 1 2 2.5 3 3.5 4
y 2.5 0.5 0.5 1.5 1.5 1.125 0
What are methods of interpolating this data, other
than using a degree 6 polynomial. Shown in the text
are the graphs of the degree 6 polynomial interpolant,
along with those of piecewise linear and a piecewise
quadratic interpolating functions.
Since we only have the data to consider, we would gen-