Mon 28 Sep: Introduction: model problem;
Cholesky factorization and fill; the graph elimination game.
[my slides,
bone density slides]
(Homework 1 assigned)
Wed 30 Sep: 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 5 Oct:
Sparse-dense and sparse-sparse triangular solves, depth-first search.
[slides]
Reading assignment: Skim Davis 6.1 (the theorems will make
more sense next week); read Davis 6.2 (LU) and 4.0 - 4.3 (Cholesky).
Wed 7 Oct:
Sparse LU and Cholesky factorizations; fill-reducing permutations.
[slides]
Reading assignment: Davis 7.6 & 7.7 (nested dissection)
and 4.4 - 4.8 & 4.11 (Cholesky).
(Homework 1 due, homework 2 assigned)
Mon 12 Oct:
Analysis of fill-reducing permutations.
[slides]
Reading assignment: Davis 7.1 - 7.4 (you can skip over
the details of AMD, though it's a nifty algorithm if you're interested)
Wed 14 Oct: (JRG travel, no class)
(Homework 2 due)
Mon 19 Oct:
Nested dissection
[same slides as last time]
Reading assignment: Davis chapter 8 (putting it all together).
(Homework 3 assigned)
Wed 21 Oct:
Direct methods grab bag.
Reading assignment:
Shewchuk paper sections 1-8 (CG),
review Saad chapter 1 (linear algebra background).
Mon 26 Oct: (JRG on jury duty, no class)
Wed 28 Oct: Iterative methods: Conjugate gradients.
[slides]
Reading assignment:
Shewchuk paper sections 1-12.
(Homework 3 due, homework 4 assigned)
Mon 2 Nov: (Aydin Buluc, guest lecturer: postponed due to flight delay).
Wed 4 Nov:
Parallel matrix-vector multiplication
[slides];
parallel sparse matrix and graph computation
[slides].
(Aydin Buluc, guest lecturer).
(Homework 4 due)
Mon 9 Nov: Convergence of CG.
[slides;
sample matrices and Matlab code].
Reading assignment:
Saad sections 10.1-10.5 (preconditioning).
Wed 11 Nov: (Veteran's Day holiday, no class)
(Final project proposals due)
Mon 16 Nov: Precondtioning; GMRES and BiCGSTAB.
[slides]
Reading assignment:
Multigrid Tutorial chapters 1 and 2 (smoothers).
Wed 18 Nov: Multigrid: smoothers.
[my slides,
Briggs et al.'s Multigrid Tutorial
slides]
Reading assignment:
Multigrid Tutorial chapters 3 and 4 (MG elements and implementation).
Mon 23 Nov: Multigrid: cycles and convergence.
Reading assignment:
Multigrid Tutorial chapters 5 (convergence) and 8 (AMG).
(Project progress reports due)
Wed 25 Nov: Algebraic multigrid. [Van Henson's AMG slides; De Sterck et al.'s paper on Markov chains]
Mon 30 Nov: Sparse eigenvalue, eigenvector, and SVD computation. [eigenvalue templates book; ARPACK software]
Wed 2 Dec: Final project presentations.
Wed 9 Dec: (Final project reports due)