3.4 Web material 47
the smallest magnitude, in some engineering applications. We may use the
singular value decomposition in this process.
The summary of the discussions about Ax = b is listed in Table 3.1.
1
1
1
1
2 0-1
-13 2
-13 2
1 -3 1
Problems
3.1. Q-R Decomposition
Find QR decomposition of A —
3.2. Least Squares Approximation: Regression
Assume that you have sampled n pairs of data of the form (x,y). Find the
regression line that minimizes the squared errors. Give an example for n=5.
3.3. Ax=b
Solve the following Ax = b using the special decomposition forms.
"132"
(a) Let Ai= 2 13
32 1
"2 13 10
(b) A 2 = 13 2 0 1
32 110
two solutions.
1 2
and b\ =
and 62 =
8"
19
3
"
8
1
19
3
(c) Az =
(d) A, =
4 5
7 8
10 11
-10 01
1 -1 00
0 1-10
0 0-11
and 63 =
using LU decomposition.
using LU decomposition. Find at least
using QR decomposition.
and 64 = using singular value decomposition.
Web material
http://abel.math.harvard.edu/~knlll/math2lb2002/10-orthogonal/
orthogonal.pdf
http://astro.temple.edu/~dhill001/modern/l-sect6-2.pdf
http://avalon.math.neu.edu/~bridger/lschwart/lschwart.html
http://ccrma-www.Stanford.edu/~j os/mdft/
