Homework 9
Math 371, Fall 2011
Assigned:
Thursday, November 10, 2011
Due:
Thursday, November 17, 2011
•
Clearly label all plots using
title
,
xlabel
,
ylabel
,
legend
•
Use the
subplot
command to compare multiple plots
•
Include printouts of all Matlab code, labeled with your name, date, and section.
•
Add 12 for page numbers in the international edition.
(1)
(Interpolating Polynomials)
The function
f
(
x
) = 1
/
(
x
+ 1)
is given at the four points
x
0
= 1
,
x
1
= 2
,
x
2
= 3
,
x
3
= 4
.
(a) Write the interpolating polynomial in Lagrange form.
(b) Write the interpolating polynomial in Newton form.
(c) Evaluate
f
(1
.
5)
and
f
(5)
using the interpolating polynomial. Which approximate value
is more accurate?
(d) Use the error formula to find an upper bound on the maximum error

f

p
3

∞
= max
1
≤
x
≤
4

f
(
x
)

p
3
(
x
)

.
(2)
(Choice of Interpolation Points)
This question investigates how different interpolation
points affect the accuracy of the interpolation. Let
f
(
x
) =
1
20
x
2
+1
.
(a) Compute and plot the interpolating polynomial for
f
(
x
)
using the equally spaced points
x
0
=

1
,
x
1
= 0
,
x
2
= 1
.
(b) The third Chebyshev polynomial is
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 Fall '08
 KRASNY
 matlab, Numerical Analysis, Legendre Polynomial, Equally Spaced Points, interpolation points, Legendre polynomial P5

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