MATH 340
LAB 6 Assignment
Lagrange’s Interpolant Polynomial using Chebyshev nodes
Last week we saw how to construct a Lagrange interpolating polynomial, given a
set of equally spaced nodes xi on an interval [a, b]. Now, instead of considering the
nodes xi as equally spaced, we use the Chebyshev nodes, defined as
xi = cos
(2i − 1)π
2n
, i = 1, 2, . . . , n (1)
The formula in (1) gives nodes that lie on [−1, 1] (and note that they are in
decrescent order on the x-axis). If we have a given interval in general form [a, b],
then we need to define the Chebyshev nodes via a transformation:
xi =
(a + b)
2
+
(b − a)
2
cos
(2i − 1)π
2n
, i = 1, 2, . . . , n (2)
Problem 1)
Repeat problems 1.1 and 1.3 from Lab 5 Assignment, by first finding the Chebyshev nodes on the given intervals. Again, plot the polynomial you obtained, the
actual function given f(x), and the data points in the same figure, and answer
the same questions about the error. Compare with the results obtained with the
equi-spaced nodes in Lab 5 and comment about your results.
Always remember to answer all questions, to significantly discuss your results,
comment your code, and put labels, title and legend in your figures to obtain full
credit for your work.
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