1
COMPUTER SCIENCE 349A
Handout Number 23
THE RUNGE PHENOMENON
The following example is the classical example to illustrate the oscillatory nature
and thus the unsuitability of high order interpolating polynomials.
It is due to Runge in
1901.
Consider the problem of interpolating
f
(
x
)
=
1
1
+
25
x
2
on the interval
[
−
1, 1]
at
n
+
1 equally-spaced points
x
i
by the interpolating polynomial
P
n
(
x
).
In the figure below, the graphs of
)
(
and
)
(
),
(
20
5
x
P
x
P
x
f
are shown.
f(x)
degree 5
degree 20
x

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*