Lecture notes for "Applied Numerical Linear Algebra"

These notes are intended to be rough outlines of the material covered during each lecture, not comprehensive notes. I will attempt to post them before lecture, but may repost them after lecture with corrections.

Lecture 1 - outline of course, beginning discussion of roundoff analysis

Lecture 2 - floating point arithmetic, roundoff analysis of polynomial evaluation, beginning discussion of vector and matrix norms

Lecture 3 - finish matrix and vector norms, geometric interpretation of condition numbers, sensitivity of solving A*x=b

(updated Sept 3, 3:15pm, after class) (updated Sept 3, 8:40am, before class)

Lecture 4 - Start Gaussian Elimination: basic algorithm, need for pivoting to keep error small, error analysis and practical error bounds

(posted Sept 8, 10:50am, before class)

Lecture 5 - We will first complete Lecture 4 (error analysis and practical error bounds), and then start discussing optimizing matrix multiplication by minimizing communication

(posted Sept 10, 6:30am, before class)

(updated Sept 14, 3:23pm)

Lecture 6: We will continue with the notes in Lecture 5 above (note that they have been updated).

We will complete the notes in Lecture 5 above, and continue with Lecture 7 - various fast matrix multiplication algorithms.

(posted Sept 17, 9:27am, before class)

For the slides illustrating Cannon's matrix multiplication algorithm, see slides 36-41 in Lecture 10 (in powerpoint) of CS267 from Spring 09

We will complete the notes in Lecture 7 above, and continue with Lecture 8 - various fast Gaussian elimination algorithms.

(posted Sept 21, 9:30pm, before class)

We will complete the notes in Lecture 08 above, and continue with Lecture 9 - Gaussian elimination for matrices with special structures.

(posted Sept 24, 11:50am, before class)

(updated Sept 28, 3:40pm)

(updated Sept 30, 4:47pm)

Lecture 10: We will continue with notes in Lecture 9 (note update above).

Lecture 11: We will still continue with notes in Lecture 9 (note update above).

Lecture 12 - We will begin Chapter 3, and try to cover sections 3.1-3.3.

(posted Oct 5, 9:20pm, before class)

(updated Oct 8, 5:50am)

(updated Oct 13, 9:50am)

Lecture 13: We will continue with the notes in Lecture 12 above (note that they have been updated).

Lecture 14: We will continue with the notes in Lecture 12 above (note that they have been updated again).

Lecture 15 - We will begin Chapter 4, and try to cover sections 4.1-4.2.

(posted Oct 15, 9:20pm, before class)

(updated Oct 20, 10:53am)

(updated Oct 22, 6:24am)

Lecture 16: We will continue with the notes in Lecture 15 above (note that they have been updated).

Lecture 17: We will continue with the notes in Lecture 15 above (note that they have been updated again).

Lecture 18 - We will begin Chapter 5.

Lecture 19 - We continue with Chapter 5. For more details about the MRRR algorithm, see the guest lecture (images of transparencies) by Prof. Beresford Parlett, and the guest lecture by Christof Voemel, both from the 2004 version of Math 221.

(posted Nov 3, before class)

(updated Nov 4, 6:49am)

After finishing the notes for Chapter 5, we will begin Chapter 6 with Lecture 21.

(posted Nov 10, before class)

(updated Nov 12, 6:25am)

(updated Nov 17, 8:15am)

(updated Nov 19, 10:45am)

(updated Nov 24, 6:55am)

Lecture 22: We will continue with the notes in Lecture 21 above (note that they have been updated).

Lecture 23: We will continue with the notes in Lecture 21 above (note that they have been updated).

Lecture 24: We will continue with the notes in Lecture 21 above (note that they have been updated).

Lecture 25: We will continue with the notes in Lecture 21 above (note that they have been updated).

Lecture 26. We will continue with Chapter 6.

(posted Dec 1, 9:00am)

Lecture 27 (powerpoint). We complete Chapter 6 with a discussion of Multigrid.