Mon 2 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)
[hw1.tex]
Wed 4 Apr: Sparse Cholesky, fill, graph game, elimination orders.
[slides;
notes and proofs;
Matlab diary;
Matlab files]
Reading for next class: Davis sections 4.0-4.7 (skim the details of 4.4-4.5)
(Cholesky, etrees) and 7.5-7.7 (nested dissection).
Mon 9 Apr: Fill-reducing permutations; sparse data structures;
matrix-matrix multiplication (SpGEMM); sparse triangular solve.
[slides]
Reading for next class: Review Davis chapter 3 (sparse triangular solve).
Read sections 6.1, 6.2, and 7.3 (LU and block triangular form).
(Homework 1 due, homework 2 assigned)
[hw2.tex]
Wed 11 Apr: More algorithms: Sparse-sparse triangular solve, LU, Cholesky.
[slides]
Reading for next class: Davis chapter 8 (sparse direct solvers).
Mon 16 Apr: Nonsymmetric matrices:
Partial pivoting, fill-reducing permutations, direct methods grab bag.
[slides1,
slides2]
Reading for next class: Shewchuk paper sections 1-8 (CG),
review Saad chapter 1 (linear algebra background).
(Homework 2 due, homework 3 assigned)
[hw3.tex]
Wed 18 Apr: Krylov subspace methods: Conjugate gradients.
[slides]
Reading for next class: Shewchuk paper sections 9-12 (convergence of CG),
Saad sections 10.1-10.6 (preconditioning).
Mon 23 Apr: Convergence of CG in theory and practice.
[slides;
Matlab diary;
Matlab files]
Reading for next class: Saad sections 6.5.1 – 6.5.4, 6.5.6 (GMRES),
6.7.1 (CG), and 7.4.2 (BiCGSTAB).
(Homework 3 due, homework 4 assigned)
[hw4.tex]
Wed 25 Apr: Preconditioning; nonsymmetric methods (GMRES and BiCGstab); high-performance implementation. [slides 1; slides 2; Matlab diary; Matlab files]
Mon 30 Apr: Graphs, Laplacians, and support-theory preconditioning.
[definitions etc. (items 1-16, 21, 23, 24, 26, 33-37, 65-67)]
Reading for next class:
Spielman survey sections 1 (intro),
2 (what Laplacians are good for), 3 (review of methods), 4 (sparse graph approximation--just scan),
5 (support theory--Monday's class), 6 (low stretch methods--Wednesday's class).
(Homework 4 due, homework 5 assigned)
[hw5.tex]
Wed 2 May: Exotic Laplacian linear solvers.
[slides;
definitions etc. (items 30, 53-54, 72-78)]
Reading for next class:
Multigrid Tutorial chapters 1 (intro), 2 (smoothers), and 3 (MG elements).
Mon 7 May: Multigrid: basics.
[my slides;
tutorial slides]
Reading for next class:
MG Tutorial chapter 4 (implementation), 5 (convergence), and optionally 8 (algebraic multigrid).
(Homework 5 due)
(Final project proposal due)
Wed 9 May: Multigrid: analysis and extensions.
[slides:
tutorial part 2;
Van Henson on AMG;
Yiannis Koutis on CMG;
Tristan Konolige on parallel AMG]
Reading for next class:
Saad sections 6.3, 6.6 (Arnoldi and Lanczos).
Mon 14 May: Sparse eigenvector methods.
[Matlab diary
and demo code;
eigenvalue templates
book;
ARPACK
and Anasazi software]
Reading for next class:
Eigenvalue templates book online nodes:
Implicitly restarted Lanczos [nodes 117 through 130].
Wed 16 May: More on eigenvector methods.
[Matlab diary
and demo code]
Reading for next class:
Wolf et al. on triangle counting.
(Progress report due)
Mon 21 May: (JRG travel, no class)
Wed 23 May: Graph algorithms and linear algebra. [slides 1, slides 2]
Mon 28 May: (Memorial Day holiday, no class)
Wed 30 May: Final project presentations. [schedule]
Mon 4 Jun: (JRG travel, no class)
Wed 6 Jun: (JRG travel, no class)
Wed 13 Jun: (Final project reports due)