Mon 5 Jan: Introduction.
Reading assignment: Benzi paper sections 1 and 2,
Templates sections
2.1 and
2.3.1.
(Optional, for more detail: Demmel chapter 6.6, pages 299-321.)
Wed 7 Jan: Krylov subspace iterations.
Class slides,
figures from Shewchuk paper.
Reading assignment: Shewchuk's
introduction to the conjugate gradient method without
the agonizing pain.
Mon 12 Jan: (Class cancelled due to illness)
Wed 14 Jan: (JRG travel, no class)
Mon 19 Jan: (Martin Luther King Day, no class)
Wed 21 Jan: Conjugate gradients: convergence, preconditioning.
Class slides (same as 7 Jan).
Reading assignment: Benzi paper sections 3.1 and 3.2 (pp. 426-437).
Mon 26 Jan: Nonsymmetric Krylov subspace methods,
intro to preconditioning.
Class slides (same as 7 Jan).
Reading assignment: Benzi paper sections 3.3 through 4 (pp. 437-448),
Templates sections
2.3.4,
2.5, and
2.6.
Wed 28 Jan: Incomplete factorization.
Class slides.
Reading assignment (optional):
Saad (either edition) 10.3 through 10.3.5 and 10.4 through 10.4.2.
Mon 2 Feb: Incomplete factorization, matrix permutations.
Class slides (same as 28 Jan),
Matlab diary.
Reading assignment: Benzi paper section 5 (pp. 448-463).
Wed 4 Feb: Nonsymmetric permutations;
sparse approximate inverse preconditioners.
Class slides (same as 28 Jan).
Reading assignment:
Chen & Toledo's paper
on experiments with support-graph preconditioners.
(See the references
for more papers on support graphs.)
Final project teams and titles due the end of this week.
Mon 9 Feb: (JRG travel, no class)
Homework 1 due.
Wed 11 Feb: (JRG travel, no class)
Mon 16 Feb: (Presidents' Day, no class)
Wed 18 Feb: Support graph preconditioning.
Class slides.
Reading assignment:
Boman & Hendrickson paper
on support theory, sections 1, 2, 3, 4, 9, and 11.
Final project initial progress reports due the end of this week.
Mon 23 Feb: Support theory.
Class slides (same as 18 Feb).
Reading assignment:
Read all of Chapter 13 (Domain Decomposition) of Saad,
except just skim the following sections:
13.3.4 (Convergence),
13.5 (Full Matrix Methods),
13.6 (Graph Partitioning).
The chapter is
online here
in files iter4.pdf or iter4.ps.
Wed 25 Feb: (SIAM PPSC meeting, no class) Homework 2 due.
Mon 1 Mar: Proofs of support graph bounds.
Class slides (same as 18 Feb).
Reading assignment: see 23 Feb.
Wed 3 Mar: Stephane Pralet on symmetric indefinite systems; introduction to domain decomposition.
Mon 8 Mar: Domain decomposition; final project presentations.
Wed 10 Mar: Final project presentations.
Final project written reports due no later than Wed 17 Mar.