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CS205 – Class 6
Reading:
Heath 3.6 (p137143), 4.7 (p202)
Numeric Linear Algebra Summary
When your matrix A is:
1.
Nonsingular use LU decomposition.
2.
Over determined use QR with Householder.
3.
Under determined use SVD.
This means some of your variables don’t have any meaning on your solution,
i.e. where you parked your car.
4.
Principal Component Analysis
a.
PCA let’s you throw away 10,000 terms and keep 6.
b.
But
don’t
use the SVD (too slow and gives you everything)! Instead, find your singular values (i.e.
i
σ
) using the power method.
Then can get eigenvectors of
A
T
A
and
AA
T
using division.
5.
For a linear system Ax=b, if the column space of A doesn’t span b, there will be no exact solution but a
least square solution. But by adding variables into the system, and thus adding corresponding columns into
A, such that the augmented column set happens to span b, the system will eventually get a unique solution.
Covered in class
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This note was uploaded on 01/05/2012 for the course CS 205A taught by Professor Fedkiw during the Fall '07 term at Stanford.
 Fall '07
 Fedkiw

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