Mon 26 Sep: Introduction: sparse linear systems;
direct and iterative methods; preconditioning.
Class slides.
Reading assignment: Shewchuk paper
sections 1-8 (through page 31). Skim sections 6 and 9.
Wed 28 Sep: Modern iterative methods: Conjugate gradient.
Class slides.
Reading assignment: Read the rest of the
Shewchuk paper through section 9.
Mon 3 Oct: Convergence of conjugate gradient.
Class slides.
Reading assignment: Saad book (either edition) sections 10.1 - 10.4.
(Homework 1 assigned.)
Wed 5 Oct: Complete and incomplete factorization. Class slides.
Mon 10 Oct: Incomplete factorization preconditioners.
Class slides.
Reading assignment: Saad book, the rest of Chapter 10.
Wed 12 Oct: Guest speaker: Viral Shah, parallel sparse matrix and graph computation. (JRG at SIMS2005)
Mon 17 Oct: Graph algorithms: matching and permutations.
Same slides as Mon 10 Oct.
(Homework 1 due.)
Wed 19 Oct: Experiments with preconditioning. Matlab diary.
Mon 24 Oct: Parallel computing and preconditioning.
Class slides.
Reading assignment:
Chen & Toledo's paper
on experiments with support-graph preconditioners.
(See the references
for more papers on support graphs.)
(Homework 2 assigned.)
Wed 26 Oct: Sparse approximate inverse preconditioners. Class slides.
Mon 31 Oct: Support graph preconditioners: construction. Class slides.
Wed 2 Nov: Support graph preconditioners: theory. Class slides (same as 31 Oct).
Mon 7 Nov: Multigrid methods: introduction.
My slides,
MG
Tutorial slides.
Reading assignment: Saad (2nd edition) sections 13.1-13.5.
(See the references
for more material on multigrid.)
(Homework 2 due,
Homework 3 assigned.)
Wed 9 Nov: Multigrid methods: V-cycle, full multigrid. MG Tutorial slides.
Mon 14 Nov: (Supercomputing 2005, no class)
Wed 16 Nov: (Supercomputing 2005, no class)
Mon 21 Nov: Multigrid methods: Algebraic multigrid.
Van
Henson's AMG slides.
(Homework 3 due.)
Wed 23 Nov: Issues with nonsymmetric matrices.
Mon 28 Nov: More on nonsymmetric matrices; final project presentations.
Wed 31 Nov: Final project presentations.
Final project written reports due no later than Wed 7 Dec.