Mon 31 Mar: Introduction: model problem;
Cholesky factorization and fill; the graph elimination game.
[slides]
(Homework 1 assigned)
Wed 2 Apr: Sparse data structures, matrix multiplication.
[slides]
Reading assignment: 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).
Mon 7 Apr:
Sparse-dense and sparse-sparse triangular solves, depth-first search.
[slides]
Reading assignment: Davis sections 4.1 - 4.7 (Cholesky).
(Homework 1 due)
Wed 9 Apr:
Sparse LU and Cholesky factorizations, pivoting, pruning.
[slides]
Reading assignment:
Davis sections 4.8, 4.11 (Cholesky), 6.1, and 6.2 (left-looking LU).
(Homework 2 assigned)
Mon 14 Apr: Sparse Cholesky analysis: elimination trees, nonzero structure prediction. [slides, row/col count paper]
Wed 16 Apr:
Fill-reducing permutations in theory and practice.
[slides]
Reading assignment:
Review Saad chapter 1 (background and notation).
(Homework 2 due, homework 3 assigned)
Mon 21 Apr:
Direct methods grab bag and wrapup.
[slides]
Reading assignment:
Shewchuk paper sections 1-5, 7, and 8.
Wed 23 Apr: Iterative methods: Conjugate gradients.
[slides]
(Homework 3 due, homework 4 assigned)
Reading assignment:
Shewchuk paper sections 1-12.
Mon 28 Apr: Convergence of CG.
[slides,
sample matrices and Matlab code,
Matlab diary from class]
Reading assignment:
Saad sections 6.1-6.3, 6.5.1-6.5.4, 6.5.6, and 6.7.1.
Wed 30 Apr: GMRES and BiCGSTAB.
[slides]
(Homework 4 due, homework 5 assigned)
Reading assignment:
Saad sections 10.1-10.4 (either edition) and 10.5 (second edition only).
Mon 5 May: (JRG travel, no class)
Wed 7 May: (JRG travel, no class)
Mon 12 May:
Preconditioning: Incomplete factorization.
[slides]
(Homework 5 due)
(Final project proposals due)
Reading assignment:
Saad sections 11.1, 11.4, 11.5, 12.1, 12.4-12.6 (parallel considerations).
Wed 14 May: Sparse approximate inverses;
parallel computing considerations.
[slides]
Reading assignment:
Saad, second edition, sections 13.1-13.5 (multigrid).
Mon 19 May: Multigrid: smoothers.
[my slides,
Briggs et al.'s Multigrid Tutorial
slides]
Reading assignment:
Saad, second edition, sections 13.6 and 13.7 (multigrid).
Wed 21 May: Multigrid: cycles and convergence.
(Project progress reports due)
Mon 26 May: (Memorial Day, no class)
Wed 28 May: Algebraic multigrid. [Van Henson's AMG Tutorial slides]
Mon 2 Jun: Support graph preconditioning. [slides]
Wed 4 Jun: Final project presentations.
Wed 11 Jun: (Final project reports due)