
# 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:

• Lectures 1-4: Sections 1.1-1.3, 2.1, 2.2, 2.3, 2.4 in Golub and van Loan. Lectures 3,4 in Trefethen
• Lectures 5-8: Sections 1.2, 2.6.1, 3.1, 5.1, 5.2, 3.2, 3.4, 4.2 in Golub and van Loan. Lecture 10 in Trefethen.
• Lectures 9-12: Sections 4.2, 2.7, 2.6, 5.3 in Golub and van Loan. Lectures 11, 12, 13, 14, 17 in Trefethen.

## 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:

• Lecture 15-20: Sections 11.2-11.4 in Golub and van Loan. Trefethen and Bau 32, 24, 27
• Lecture 20-24: Saad Section 6.3-6.5, Trefethen Lecture 33, 35
• Lecture 25: Saad 6.72, Golub and van Loan 10.3.6
• Lecture 26: Trefethen and Bau, Lecture 40, Golub and van Loan 11.5
• Lecture 27-28: Trefethen and Bau, Lecture 26, 28