Lecture 16.
Stability, Gaussian Elimination with Partial
Pivoting
To I discussed the difference between the notion
of ill-conditioned input and an unstable algorithm. The message of the day was
that Gaussian Elimination without pivoting is un-stable, but with partial
pivoting is stable. We saw a small example that illustrated an extreme case
where pivoting made a huge difference in the accuracy of LU factorization of a
matrix.
I quickly reviewed how
permutation matrices are used to keep track of pivoting when performing LU
factorization.
I also gave a short
demonstration of some of the m-files that accompany our text. I also showed how
some MATLAB commands could be used to solve systems of linear equations.
On Thursday I plan to review for quiz
number 2 which will be held on
Friday.
Our treatment of linear algebra
and solving linear equations is covered in Chapters 7 and 8 of NMM. The sections
to focus on are: sections 7.1 and 7.2 in Chapter 7. in particular the treatment
of vector and matrix norms, and 7.3.1 linear independence. In Chapter 8 you
should read Section 8.1 - 8.3 and sections 8.4.1 and 8.4.3. You can skip section
8.4.2 and section 8.5.
In the Ellis
notes you can read classes 26 and 27. Class 28 has a slightly different
treatment of error analysis. Class 29 covers LU decomposition.
Posted: Tue - October 19, 2004 at 06:56 PM