Course Information

Day One Handout

The course meets in slot 07, from 2:00-2:50 PM on Mondays, Wednesdays, and Fridays, in C 2024. My office hours are TBA, in HH-2019.

Textbook
No textbooks are required for this course. Relevant e-books from the library's collection include:

  • Iterative methods for sparse linear systems by Saad (full text pdf available here)
  • Iterative methods for solving linear systems by Greenbaum
  • Matrix iterative analysis by Varga
  • Finite elements and fast iterative solvers with applications in incompressible fluid dynamics by Elman, Silvester, and Wathen
  • Iterative methods for linear systems: theory and applications by Olashanskii and Tyrtyshnikov
  • A multigrid tutorial by Briggs, Henson, and McCormick
  • An introduction to domain decomposition methods: algorithms, theory, and parallel implementation by Dolean, Jolivet, and Nataf

    D2L
    This course will not be using D2L; all material online will be posted here.
  • Approximate Schedule



  • 1/6: Introduction, Finite-Difference Discretization (review), HW1 distributed
  • 1/8: Costs of Gaussian Elimination
  • 1/11: Envelope of factorization, permutations
  • 1/13: Graph models, Cuthill-McKee
  • 1/15: Elimination graphs, minimum degree
  • 1/18: Nested dissection
  • 1/20: Intro to iterative methods
  • 1/22: Matrix splittings, Jacobi, Gauss-Seidel, SOR
  • 1/25: Convergence of stationary iterations
  • 1/27: Stein-Rosenberg and Ostrowski-Reich theorems
  • 1/29: Convergence of SOR, HW2 distributed
  • 2/1: Incomplete Factorization
  • 2/3: Chebyshev iteration
  • 2/5: Convergence of Chebyshev, nonsymmetric case
  • 2/8: Class cancelled
  • 2/10: Class cancelled
  • 2/12: Class cancelled
  • 2/15: Arnoldi and GMRES, Part I
  • 2/17: Arnoldi and GMRES, Part II
  • 2/19: Lanczos and MINRES, HW3 distributed
  • 2/22: Makeup Class, Conjugate Gradient
  • 2/24: Makeup Class, Preconditioning
  • 2/26: Makeup Class, Faber-Manteuffel Theorem, BiLanczos and BiCG
  • 2/29: CGS and BiCGStab
  • 3/2: Additive Schwarz
  • 3/4: Multiplicative Schwarz, Schur Complement Methods
  • 3/7: Overlapping DD, Restricted Additive Schwarz
  • 3/9: Optimized Schwarz
  • 3/11: Two-level methods, Part I
  • 3/14: Two-level methods, Part II
  • 3/16: Smoothing Property
  • 3/18: Coarse-grid correction, two-grid algorithm
  • 3/21: No class
  • 3/23: No class
  • 3/25: No Class: Good Friday
  • 3/28: Multigrid V-cycle
  • 3/30: Effectiveness of the V-cycle
  • 4/1: Multigrid and refined meshes
  • 4/4: Comparing domain decomposition and multigrid
  • 4/6: Final project presentations