Math 432 - Numerical Linear Algebra - Fall 2013
Homework 2
Assigned: Friday, September 6, 2013
Due: Friday, September 13, 2013
Include a cover page and a problem sheet.
1. Verify that the l -norm
|x| = max |xi |
1in
satises the properties of a vector nor
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 12
Assigned: Sunday, December 8, 2013
Due: Friday, December 13, 2013
1. Apply the Gergorin disk theorems to obtain bounds for the eigenvalues of the
s
following matrices:
10 1 1
(a) A = 2 10 1 ,
2 2
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 11
Assigned: Saturday, November 29, 2013
Due: Friday, December 6, 2013
Use the following data for both problems:
(i) A randomly generated matrix of order 100.
(ii) Hilbert matrix of order 20.
1 1 1
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 1
Assigned: Friday, August 30, 2013
Due: Friday, September 6, 2013
Include a cover page and a problem sheet.
0. Give a brief description of your academic background and research interests. If
you w
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 8
Assigned: Saturday, November 2, 2013
Due: Friday, November 8, 2013
1. Using the Matlab command qr, nd the QR factorization of
1 2
A = 3 4.
5 6
For this matrix and with vector b = ( 1 2 3 )T , usin
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 6
Assigned: Saturday, October 5, 2013
Due: Friday, October 11, 2013
Include a cover page and a problem sheet.
Include all of your scripts and output results.
Place a comment at the top of each fu
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 9
Assigned: Saturday, November 9, 2013
Due: Friday, November 15, 2013
1. (a) Using the Matlab command svd, nd the SVD of the following matrices:
1 2
A = 3 4,
5 6
A = (1 2 3)
1
A = 1
1
A = diag (
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 7
Assigned: Saturday, October 26, 2013
Due: Friday, November 1, 2013
Include a cover page and a problem sheet.
Include all of your scripts and output results.
Place a comment at the top of each f
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 3
Assigned: Friday, September 13, 2013
Due: Friday, September 20, 2013
Include a cover page and a problem sheet.
1. Let = 10, t = 4. Compute fl(AT A), where
1
4
10
0
1
0 .
104
Repeat your computa
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 4
Assigned: Friday, September 20, 2013
Due: Friday, September 27, 2013
Include a cover page and a problem sheet.
1. (# 4.3 (c) Show that the roots of the polynomial (x 1)(x 0.99)(x 2) are
ill-condi
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 5
Assigned: Saturday, September 28, 2013
Due: Friday, October 4, 2013
Include a cover page and a problem sheet.
Include all of your scripts and output results.
Place a comment at the top of each
Math 432 - Numerical Linear Algebra - Fall 2013
Homework 10
Assigned: Sunday, November 17, 2013
Due: Friday, November 22, 2013
1. (a) Prove that AT A is symmetric and positive denite if and only if A has full
rank.
(b) Let x be the least-squares solution