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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
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This note was uploaded on 12/16/2011 for the course MATH 371 taught by Professor Krasny during the Fall '08 term at University of Michigan.
 Fall '08
 KRASNY
 matlab

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