Support-Preconditioning Materials and Publications

Here is a tentative agenda for the five days of the course. The list includes the topics that I plan to cover each day (this corresponds to the lecture notes) and the exercise for that day.

  1. Introduction + Graphs/Matrices/Laplacians
    Exercise: An interesting application of Laplacians 
                     + first part of augmented spanning trees exercise
  2. Iterative solvers
    Exercise: dropping a few edges
                     + second part of augmented spanning trees
  3. Sparse direct solvers
    Exercise: banded and low-profile matrices
                     + third part of augmented spanning trees
  4. Support theory and spectral bounds + graph embeddings + augmented spanning trees
    Exercise: last part of augmented spanning trees
  5. Finite elements by element approximations + finite-elements by fretsaw + advanced topics
    excercise: diagonally-dominant approximations

Lecture Notes (please do not redistribute)


Here are the Matlab files that you will need for the exercises.

Core publications

Finite Elements

Matrices and Graphs

Sophisticated Graph Algorithms for Constructing Preconditioners

Some non-preconditioning applications