# Lecture Plan

**Note:** YS Chapter 2 is about Discretization of Partial Differential Equations. This is not part of the curriculum for this course, but many examples of equations we want to solve stem from discretizations of PDE's. If you are not familiar with finite difference methods, it is recommended to read 2.1-2.2.

Week | Dates | Topics | Reading | Other |
---|---|---|---|---|

34 | 19.08-25.08 | Introduction Linear Algebra | YS 1.1-1.9,1.13 | |

35 | 26.08-01.09 | Sparse Matrices Basic Iterative Methods | YS 3.1,3.4-5 YS 4.1,4.2 | |

36 | 02.09-08.09 | Fast Poisson Solvers Projection Methods | Rønquist: The Poisson problem in \(\mathbb{R}^2\):diagonalization methods YS 1.11-12,5.1-3 | |

37 | 09.09-15.09 | Krylov Subspace Methods Arnoldi, FOM | YS 6.1-4 | |

38 | 16.09-22.09 | IOM, GMRES | YS 6.4.1-2, 6.5.1-5 | Project 1 due 22.09 |

39 | 23.09-29.09 | Lanczos, D-Lanczos, Conjugate Gradient | YS 6.6-6.7 | |

40 | 30.09-06.10 | Convergence analysis for Krylov subspace methods | YS 6.11 | |

41 | 07.10-13.10 | Idea of preconditioning, preconditioned Conjugate Gradient, examples of preconditioners | YS 9.1,9.2, 10.1-10.2, 10.3.1-3 | |

42 | 14.10-20.10 | Multigrid methods | YS 13.1-4 | Project 2 due 20.10 |

43 | 21.10-27.10 | Eigenvalue problems: Overview, power iteration, Rayleigh quotient. | TB 25,27 | |

44 | 28.10-03.11 | Reduction to Hessenberg form. Basic QR algorithm, QR with shift | TB 26,28,29 | |

45 | 04.11-10.11 | Singular Value Decomposition | Lecture notes. Jupyter Notebook on SVD | |

46 | 11.11-17.11 | No lectures | Project 3 due 17.11 | |

47 | 18.11-24.11 | Monday: Summary, Thursday: Question session |

- YS:
*Saad*Iterative Methods for Sparse Linear Systems. - TB:
*Trefethen and Bau*Numerical Linear Algebra. Copies of the relevant chapters can be found on Blackboard.