Lecture plan
The lecture plan will be continuously updated.
Date  Topics  Reading 

Introduction and basics of linear algebra  
Week 34  Introduction Inner products, norms, and matrix norms Orthogonality and QRdecomposition  YS 1.11.7 TB 10 
Week 36  QRdecomposition Jordan and Schur canonical forms Normal and Hermitian matrices Values of a matrix CourantFischer Theorem Positive definite matrices  TB 10 YS 1.8 (not 1.8.4), 1.9, 1.11 
Solving Poisson equations  Einar Rønquist's note Please read YS 2.22.2.5 if you are not familiar with finite difference methods. 

Week 37  Fast Poisson solvers Perturbation analysis  Einar Rønquist's note YS 1.13.2 
Basic iterative methods for linear systems  
Jacobi, GaussSeidel, and SOR Convergence analysis  YS 4.1, 4.2  
Week 38  Basics of projection methods Steepest Descent and MR  YS 5.1, 5.2, 5.3 
Krylov subspace methods  
Krylov subspaces  YS 6.2  
Week 39  More on Krylov subspaces Projection operators Arnoldi's method FOM, IOM, DIOM  YS 1.12, 6.1, 6.2, 6.3 
Week 40  GMRES, QGMRES Symmetric Lanczos algorithm CG method  YS 6.5.16.5.7, 6.6, 6.7 
Week 41  CG method Convergence of CG and GMRES Idea of preconditioning Examples of preconditioners  YS 6.11, 10.1, 10.2 
Week 42  Preconditionend GMRES PCG  YS 10.1 
Multigrid and domain decomposition  
Basics of multigrid methods Weighted Jacobi method Prolongation and interpolation Vcycles and Wcycles  YS 13.113.4  
Week 43  Vcycles Redblack GaussSeidel method Multigrid as preconditioner Domain decomposition Additive and multiplicative Schwarz sweeps Project assignment  YS 13.4, 12.4.112.4.2, 14.1, 14.3 
Singular value and eigenvalue decompositions  
Week 44  Singular value decomposition (SVD) Matrix properties via the SVD SVD and matrix inversion  TB4, TB5 GvL 2.5.2, note on the SVD 
Week 45  Truncated SVD Regularisation Similarity transforms and eigenvalues Reductions to Hessenberg form Power method and inverse power method  note on the SVD, TB2527 
Week 46  Rayleigh quotient iteration Simultaneous power method QRmethod for eigenvalue computations QRmethod with shifts  TB2729 
Summary  
Week 47  Summary of the lecture (Monday) Question session (Wednesday) 
YS refers to the book Iterative Methods for Sparse Linear Systems by Yousef Saad.
TB refers to the book Numerical Linear Algebra by L. N. Trefethen and D. Bau; GvL refers to the book Matrix Computations by G. Golub and C. Van Loan. Scans of the chapters used in the course can be found on itslearning.