Lecture notes for "Applied Numerical Linear Algebra", Fall 2010

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.
  • Aug 26: Lecture 1 - outline of course, begin discussion of roundoff in the context of polynomial evaluation
  • Posted before class, updated after class at 12pm, Aug 26
  • Aug 31: Lecture 2 - floating point arithmetic and rounding errors
  • Posted before class, 6:11am; updated (slightly) 8/31, 1:36 pm
  • Sep 2: Lecture 3 - vector and matrix norms, Singular Value Decomposition, condition number for solving Ax=b
  • Posted before class, Sep 1, 12:15pm
  • Updated Sep 6, 2pm; Sep 7, 6:22am; Sep 9, 6:50am
  • Sep 7: Continue with Lecture 3 (note updates above)
  • Sep 9: Complete Lecture 3 (note updates above)
  • Sep 14: Lecture 6 - fast algorithms for matrix multiplication
  • Posted before class, Sep 14, 6:55am
  • Updated Sep 14, 4:40pm
  • Updated Sep 21, 6:36am
  • Updated Sep 21, 9:00am
  • Sep 16: Continue with Lecture 6 (note updates above)
  • For the pictures of Cannon's Algorithm presented in class, please see slides 47-49 of Lecture 13 (ppt) of CS267 from Spring 2010.
  • For the proof of the Loomis-Whitney inequality used in class, see slide 16 of Lecture 3 of my short course on "Minimizing communication in numeerical linear algebra," which was part of the International Summer School on Numerical Linear Algebra
  • Sep 21: complete Lecture 6 (note updates above), begin Lecture 8 on solving linear systems with Gaussian Elimination.
  • Posted before class, Sep 21, 6:30am
  • Updated, Sep 22, 8:45pm
  • Sep 23: complete Lecture 8 (note updates above) begin Lecture 9 on solving linear systems with special structures.
  • Posted before class, Sep 23, 5:40am
  • Updated, Sep 29, 8:40pm
  • Updated, Sep 30, 6:10am
  • Sep 28: continue Lecture 9 (note updates above)
  • Sep 30: complete Lecture 9 (note updates above) begin Lecture 11 on minimizing communication in Gaussian Elimination.
  • Posted before class, Sep 29, 10:05pm
  • Updated, Sep 30, 6:15am
  • Updated, Oct 4, 11:45am
  • Oct 5: continue Lecture 11 (note updates above)
  • Oct 7: complete Lecture 11, begin Lecture 13 on least squares problems
  • Posted before class, Oct 7, 6:30am
  • Updated, Oct 7, 1:00pm
  • Updated, Oct 11, 6:30pm
  • Updated, Oct 12, 5:10am
  • Oct 12: continue Lecture 13 (note updates above)
  • Oct 14: continue Lecture 13 (note updates above)
  • Oct 19: complete Lecture 13 (note updates above), and begin Lecture 16 on eigenvalue problems.
  • Posted before class, Oct 19, 9:10am
  • Updated, Oct 21, 6:25am
  • Updated, Oct 26, 6:50am
  • Updated, Oct 27, 5:10pm
  • Oct 21: continue Lecture 16 (note updates above)
  • Oct 26: continue Lecture 16 (note updates above)
  • Oct 28: complete Lecture 16 (note updates above), and begin Lecture 19 on symmetric eigenvalue problems (Chapter 5)
  • Posted before class, Oct 27, 8:37pm
  • Updated, Nov 2, 7:00am
  • Updated, Nov 3, 6:45am
  • Nov 2: continue Lecture 19 (note updates above)
  • Nov 4: continue Lecture 19 (note updates above)
  • Nov 9: begin Lecture 22 on iterative methods
  • Posted before class, Nov 9, 6:00am
  • Updated , Nov 18, 7:25am
  • Updated , Nov 18, 9:00am
  • Updated , Nov 22, 5:08pm
  • Updated , Nov 22, 9:30pm
  • Updated , Nov 23, 5:15am
  • Nov 16: continue Lecture 22 (note updates above)
  • Nov 18: continue Lecture 22 (note updates above)
  • Nov 23: complete Lecture 22 (note updates above) and begin Multigrid (notes in ppt or pdf)
  • Posted before class, Nov 23, 5:50am
  • Updated, Nov 28, 1:40pm
  • Updated, Nov 29, 8:30pm