Mon 1 Apr: Introduction: model finite difference problem;
graph Laplacians.
[slides;
Matlab diary;
Matlab files]
Reading for next class: Review Davis chapter 1 (definitions).
Read chapter 2 (you don't have to read all the code in detail)
and chapter 3 (sparse triangular solves).
(Homework 1 assigned)
Wed 3 Apr: Sparse Cholesky, fill, graph game, elimination orders.
[slides;
Matlab diary;
Matlab files]
Reading for next class: Davis sections 4.0-4.1 (Cholesky, etrees)
and 7.5-7.7 (nested dissection).
Mon 8 Apr: Analysis of fill-reducing permutations;
nested dissection and graph partitioning.
[slides updated from last time;
class notes;
Matlab diary]
Reading for next class: Davis sections 4.2, 4.3, 4.6, 4.7, 4.11;
skim sections 4.4, 4.5, and 4.8.
(Homework 1 due, homework 2 assigned)
Wed 10 Apr: Data structures and algorithms: SpGEMM, Cholesky, LU without pivoting.
[slides]
Reading for next class: Review Davis chapter 3; read sections 6.1, 6.2, and 7.3.
Mon 15 Apr: (JRG travel, no class) [class notes for April 8 and 10]
Wed 17 Apr: (JRG travel, no class)
Mon 22 Apr: Sparse triangular solves, LU with partial pivoting, nonsymmetric matrix permutations.
[slides continued from last time;
new slides]
Reading for next class: Davis chapter 8.
(Homework 2 due)
Wed 24 Apr: Direct methods grab bag.
[slides on supernodes for cache,
parallel methods,
block triangular form and Dulmage-Mendelsohn;
Matlab diary]
Reading for next class:
Shewchuk paper sections 1-8 (CG),
review Saad chapter 1 (linear algebra background).
(Homework 3 assigned)
Mon 29 Apr: Krylov subspace methods: Conjugate gradients.
[slides]
Reading for next class:
Shewchuk paper sections 1-12.
Wed 1 May: Analysis and convergence of CG.
[same slides as last time]
Reading for next class: Saad sections 10.1 - 10.5 (preconditioning);
optional: sections 6.5.1 – 6.5.4, 6.5.6 (GMRES), 6.7.1 (conjugate gradients), and 7.4.2 (BiCGSTAB).
(Homework 3 due, homework 4 assigned)
Mon 6 May: CG convergence experiments.
[Matlab diary]
Reading for next class:
Toledo & Avron:
Read sections 12.1, 12.2, 12.3 (but don't get bogged down in all the details), and 12.5.
Browse the definitions and theorems in 12.4 only as necessary to understand 12.5.
Chen & Toledo:
Read sections 1, 2.1, and 4; browse the experimental results in 3.
There's also an excellent concise set of
lecture notes by Dan Spielman.
Wed 8 May: GMRES and BiCGstab; preconditioning
[slides on preconditioning
and parallel matvec;
Matlab diary]
(Homework 4 due, homework 5 assigned)
Mon 13 May: Graphs, Laplacians, and support-theory preconditioning.
[updated slides]
Reading for next class:
SpGEMM paper
sections 1 - 4 and 6; skim section 5 (experimental results).
(Final project proposals due)
Wed 15 May: Graph algorithms and linear algebra.
[I didn't get to any of this, but here are the slides anyway]
Reading for next class:
Multigrid Tutorial chapters 1 (intro), 2 (smoothers), and 3 (MG elements).
(Homework 5 due)
Mon 20 May: Multigrid: basics.
[my slides;
tutorial slides]
Reading for next class:
MG Tutorial chapter 4 (implementation), 5 (convergence), and optionally 8 (algebraic multigrid).
Wed 22 May: Multigrid: analysis and extensions.
[MGT slides part 2;
Van Henson's slides on algebraic multigrid;
a paper on multigrid for Markov chains]
Reading for next class: Saad sections 6.3, 6.6 (Arnoldi and Lanczos).
(Project progress reports due)
Mon 27 May: (Memorial Day holiday, no class)
Wed 29 May: Sparse eigenvector methods. [Matlab diary and demo code; eigenvalue templates book; ARPACK and Anasazi software]
Mon 3 Jun: Final project presentations. [schedule]
Wed 5 Jun: Final project presentations. [schedule]
Wed 12 Jun: (Final project reports due)