EE 103 HW 4 Spring 2010 Prof. S.E. Jacobsen
1
EE103 Applied Numerical Computing, Spring 2010
HW 4
Due: 5 /3/2010 (Beginning
of Lecture)
Your HW answers must contain your ID, Last Name, First Name, and the number of the
Discussion Section in which you are enrolled (by the way, you’re free to attend other
Sections as well).
Class:
The purpose of HWs is absolutely NOT for the mere assignment of grades.
The
purpose of HW assignments is to engage the student in the process of learning the material
of the course and the material that the instructor believes to be instructive.
As such, your
work must be your own and reflect your effort in the learning process.
As a result, you are not to consult the notes, HWs, HW solutions, etc., of other courses or
past offerings of this course.
Of course, you may discuss the material of this course with
other students of this class; however, your work must be your own.
A violation of the latter
may be considered to be an act of academic dishonesty.
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All work that involves Matlab programming and output
must
be submitted, hard copy,
using Matlab’s “diary” command (e.g., “diary myproblem.txt”).
Matlab’s edit, or any
other text editor, can be used to include your name, ID, Problem number, comments, etc.
Problem 1:
Given an
x
nn
nonsingular
A
, and
any
x
singular matrix
B
, the following can be shown:
A
cond A
AB
(1)
Note that (1)
implies that
singular
sup
B
A
cond A
(2)
(actually, it can be shown that equality holds).
This implies that
()
cond A
is essentially a
measure of how close
A
is to being a singular matrix (you may regard “sup” as a replacement
for “max”).