Lecture notes for "Applied Numerical Linear Algebra", Fall 2023

Lectures will be recorded, and posted in .mp4 (video) format on bcourses.berkeley.edu, These lectures will be recordings of me speaking, writing on a "virtual whiteboard", and occasionally displaying prepared figures, powerpoint, or doing live Matlab demonstrations. We will try to post typed course notes before each lecture (in .txt and .pdf), and a pdf of the "virtual white board" after each on-line class meeting. One "lecture" covers one topic, which might take more than one 50-minute class meeting. You can find all the notes and virtual white boards from the last offering in Spr 22 here.

In addition, a student generously typed up all the class notes from this last offering in latex. These notes, which may turn into a new edition of the textbook, have not been proofread, so are only posted on bcourses, under files as ma221_scribed_notes.pdf. Suggested comments or corrections are welcome, in any of these materials!

If I notice any minor mistakes in the virtual whiteboard after recording, I will correct them before posting, using red ink to make changes easier to see. I will also indicate below the relevant sections of the textbook to read.
  • Aug 23: Lecture 1: Course Outline
  • Typed notes, in .txt and .pdf (updated 8/23, 8:58am)
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (2.5MB)
  • Textbook: read sections 1.1, 1.2, 1.3
  • Aug 25: Lecture 2: Continue Course Outline
  • Same typed notes as above, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (3.3MB)
  • Textbook: read sections 1.1, 1.2, 1.3
  • Aug 28: Lecture 3: Finish Course Outline, start Floating Point Arithmetic and Error Analysis
  • Finish typed notes above, and start new ones in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (1.9MB)
  • Textbook: read sections 1.4, 1.5, 1.6
  • Aug 30: Lecture 4: Continue Floating Point Arithmetic and Error Analysis
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (2.2MB)
  • Textbook: read sections 1.4, 1.5, 1.6
  • Sep 1: Lecture 5: Finish Floating Point Arithmetic and Error Analysis, start Norms, the SVD, and condition numbers for Ax=b
  • Finish typed notes above, start new ones in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (2.4MB)
  • Textbook: read sections 1.7, 3.2.3, 2.2 (2.2.1, 2.4.3 and 2.4.4 are optional)
  • Sep 6: Lecture 6: Continue Norms, the SVD, and condition numbers for Ax=b
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (2.5MB)
  • Textbook: read sections 1.7, 3.2.3, 2.2 (2.2.1, 2.4.3 and 2.4.4 are optional)
  • Sep 8: Lecture 7: Continue Norms, the SVD, and condition numbers for Ax=b
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (2.0MB)
  • Textbook: read sections 1.7, 3.2.3, 2.2 (2.2.1, 2.4.3 and 2.4.4 are optional)
  • Sep 11: Lecture 8: Finish Norms, the SVD, and condition numbers for Ax=b, start Real cost of an algorithm, and Matrix Multiplication
  • Finish typed notes as above, start new ones in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (2.5MB)
  • Textbook: read sections 2.6.1 and 2.6.2. See also links on the class web page under "References for Communication-Avoiding Algorithms" for more recent results
  • Sep 13: Lecture 9: Continue Real cost of an algorithm, and Matrix Multiplication
  • Same typed notes as above, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, in .pdf (2.6MB)
  • Textbook: read sections 2.6.1 and 2.6.2. See also links on the class web page under "References for Communication-Avoiding Algorithms" for more recent results, and the scribed notes posted on bcourses
  • Sep 15: Lecture 10: Finish Real cost of an algorithm, and Matrix Multiplication
  • Same typed notes as above, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.5MB)
  • Textbook: read sections 2.6.1 and 2.6.2. See also links on the class web page under "References for Communication-Avoiding Algorithms" for more recent results, and the scribed notes posted on bcourses
  • Sep 18: Lecture 11: Start Gaussian Elimination
  • Typed notes, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (3MB)
  • Textbook: read sections 2.3, 2.4.1, 2.4.2, 2.4.4, 2.6.3
  • Sep 20: Lecture 12: Continue Gaussian Elimination
  • Same typed notes as above, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.8MB)
  • Textbook: read sections 2.3, 2.4.1, 2.4.2, 2.4.4, 2.5, 2.6.3
  • Sep 22: Lecture 13: Finish Gaussian Elimination, start Gaussian Elimination for matrices with special structures
  • Finish typed notes above, then start .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.6MB)
  • Textbook: read section 2.7
  • Sep 25: Lecture 14: Continue Gaussian Elimination for matrices with special structures
  • Same typed notes as above, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.7MB)
  • Textbook: read section 2.7
  • Sep 27: Lecture 15: Continue Gaussian Elimination for matrices with special structures
  • Same typed notes as above, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (1.8MB)
  • Textbook: read section 2.7
  • Sep 29: Lecture 16: Continue Gaussian Elimination for matrices with special structures
  • Same typed notes as above, in .txt and .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.3MB)
  • Textbook: read section 2.7
  • Oct 2: Lecture 17: Finish Gaussian Elimination for matrices with special structures, start Least Squares
  • Finish typed notes above, and start new ones in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.8MB)
  • Textbook: read sections 3.1-3.4
  • Oct 4: Lecture 18: Continue Least Squares
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.3MB)
  • Textbook: read sections 3.1-3.4
  • Oct 6: Lecture 19: Finish Least Squares
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.1MB)
  • Textbook: read sections 3.1-3.4
  • Oct 9: Lecture 20: Start Low-Rank Matrices and Randomized Algorithms
  • Typed notes, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.8MB)
  • Textbook: read section 3.5. See also the References for Randomized Algorithms on the class web page.
  • Oct 11: Lecture 21: Continue Low-Rank Matrices and Randomized Algorithms
  • Typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.6MB)
  • Textbook: read section 3.5. See also the References for Randomized Algorithms on the class web page.
  • Oct 13: Lecture 22: Continue Low-Rank Matrices and Randomized Algorithms
  • Typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (3.1MB)
  • Textbook: read section 3.5. See also the References for Randomized Algorithms on the class web page.
  • Oct 16: Lecture 23: Finish Low-Rank Matrices and Randomized Algorithms, start Eigenvalue Problems
  • Finish typed notes above, start new ones in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.7MB)
  • Textbook: read Chap 4.
  • Oct 18: Lecture 24: Continue Eigenvalue Problems
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.6MB)
  • Textbook: read Chap 4.
  • Oct 20: Lecture 25: Continue Eigenvalue Problems
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.9MB)
  • Textbook: read Chap 4.
  • Oct 23: Lecture 26: Continue Eigenvalue Problems
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.2MB)
  • Textbook: read Chap 4.
  • Oct 25: Lecture 27: Continue Eigenvalue Problems
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.1MB)
  • Textbook: read Chap 4.
  • Oct 27: Lecture 28: Finish Eigenvalue Problems, start Symmetric Eigenvalue Problems and SVD
  • Finish typed notes above, start new ones in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.4MB)
  • Textbook: read Chap 5.
  • Oct 30: Lecture 29: Continue Symmetric Eigenvalue Problems and SVD
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.4MB)
  • Textbook: read Chap 5.
  • Nov 1: Lecture 30: Continue Symmetric Eigenvalue Problems and SVD
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.9MB)
  • Textbook: read Chap 5.
  • Nov 3: Lecture 31: Continue Symmetric Eigenvalue Problems and SVD
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.6MB)
  • Textbook: read Chap 5.
  • Nov 6: Lecture 32: Finish Symmetric Eigenvalue Problems and SVD,
    start Introduction to Iterative Methods for Ax=b and Ax = lambda x
  • Finish typed notes above, start new ones in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.9MB)
  • Textbook: read Sections 6.1 through 6.4
  • Nov 8: Lecture 33: Continue Introduction to Iterative Methods for Ax=b and Ax = lambda x
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.5MB)
  • Textbook: read Sections 6.1 through 6.4
  • Nov 13: Lecture 34: Finish Introduction to Iterative Methods for Ax=b and Ax = lambda x
  • This lecture will only be posted here, and not given in person, since I will be away at a conference on Nov 13
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.1MB)
  • Textbook: read Sections 6.1 through 6.4
  • Nov 15: Lecture 35: Start Splitting Methods
  • Typed notes, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.6MB)
  • Textbook: read Sections 6.5.1 through 6.5.5
  • Nov 17: Lecture 36: Continue Splitting Methods
  • Same typed notes as above, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.2MB)
  • Textbook: read Sections 6.5.1 through 6.5.5
  • Nov 20: Lecture 37: Finish Splitting Methods, start Multigrid
  • Same typed notes as above, in .txt and .pdf,
  • Powerpoint slides for Multigrid, in .pdf
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (1.2MB)
  • Textbook: read Section 6.9
  • Nov 27: Lecture 38: Start Krylov Subspace Methods
  • Typed notes, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.9MB)
  • Textbook: read Section 6.6 through the end of 6.6.1.
  • Nov 29: Lecture 39: Krylov Subspace Methods: GMRES and CG
  • Typed notes, in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.5MB)
  • Textbook: read Sections 6.6.2, 6.6.3 and 6.6.6
  • Dec 1: Lecture 40: Finish CG, then Preconditioning
  • Finish typed notes above, start new ones in .txt and .pdf,
  • Recorded lecture: posted on bcourses.berkeley.edu
  • Recorded virtual whiteboard, .pdf (2.5MB)
  • Textbook: read Sections 6.6.5 and 6.10