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Homework 7
Math 371, Fall 2011
Assigned:
Saturday, October 28, 2011
Due:
Thursday, November 3, 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)
(Condition numbers)
For two
n
×
n
matrices
A
and
B
, prove that (
AB
)

1
=
B

1
A

1
,
and (
αA
)

1
=
1
α
A

1
. Now do P. 187 #1, 2.
(2)
(Residual errors vs. forward errors)
As in the previous homework, let
A
be the
n
×
n
matrix of the form
2

1

1
2

1

1
2
.
.
.
.
.
.
.
.
.

1

1
2
.
Write a matlab function named
[rerr, ferr, condnum] = ResidualFwdErrors(n)
which
takes
n
as an argument, generates the matrix
A
as above, and then a vector
x
, and then
a vector
b
=
Ax
, and returns the relative residual error, relative forward error, and the
condition number.
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 Fall '08
 KRASNY
 matlab

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