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Matrix Computations

David Gleich

Purdue University

Fall 2017

Course number CS-51500

Tuesday and Thursday, 10:30-11:45am

Location Forney B124


Course schedule

The overall course breaks down into two units (i) dense matrix computations and (ii) sparse and large-scale matrix computations.

A tentative list of lectures and readings follows.
Please see the readings page for an up to date list of course materials.

Unit 1 - Dense matrix computations

  1. Aug 22 - Introduction (syllabus)
  2. Aug 24 - Survey due Basics and Julia
  3. Aug 29 - Norms and geometry, invertible matrices
  4. Aug 31 - matrix norms, orthogonal matrices, the SVD
  5. Sept 5 - Building a search engine with matrices, more SVD, linear systems
  6. Sept 7 - QR decompositions of a matrix
  7. Sept 12 - Using linear systems to rank sports teams, LU factorization
  8. Sept 14 - More LU, pivoting, flop count for LU
  9. Sept 19 - Cholesky factorization, flops of Cholesky
  10. Sept 21 - Numerical stability, error analysis
  11. Sept 26 - Stability of variance computations, least squares
  12. Sept 27 - Flex class.
  13. Oct 3 - Review for midterm and review HW
  14. Oct 5 - In class
    Oct 10 Fall break

A rough reading guide would be:

Unit 2 - Sparse and large-scale matrix computations

  1. Oct 12 - Sparse storage formats, sparse matrix-vector products
  2. Oct 17 - Residuals and linear systems, Jacobi and Gauss-Seidel
  3. Oct 19 - Convergence of Jacobi, eigenvalues
  4. Oct 24 - Methods to compute eigenvalues, PageRank
  5. Oct 26 - Gauss-Seidel and preoprty A, SOR and Richardson
  6. Oct 31 - Basics of Arnoldi
  7. Nov 2 - GMRES, Krylov
  8. Nov 7 - Arnoldi, GMRES, Krylov
  9. Nov 9 - Lanczos and Conjugate Gradient
  10. Nov 14 - Orthogonal polynomials and CG
  11. Nov 16 - GMRES and Mod. Gram Schmidt
  12. Nov 21 - Reduction to tridiagonal form for eigenvalues
    Nov 23 - Thanksgiving break
  13. Nov 28 - Preconditioning and CG convergence
  14. Nov 30 - Kronecker products and the Laplacian
  15. Dec 5 - Optimal SOR omega,
  16. Dec 7 - Final class!

A rough reading guide would be: