https://venkovic.github.io/NLA-for-CS-and-IE.html

Nicolas Venkovic

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Numerical Linear Algebra for Computational Science and Information
Engineering (CITHN2006)

Home, Research, Teaching

The course is organized into 18 lectures. All lectures consist of a
theoretical presentation followed by homework problems [pdf]. Most
lectures are also followed by Julia coding assignments.

00. Introduction
    slides [tex, pdf]

01. Essentials of linear algebra
    slides [tex, pdf]

02. Essentials of the Julia language
    slides [tex, pdf]

03. Floating-point arithmetic and error analysis
    slides [tex, pdf], notebook [ipynb, pdf]

04. Direct methods for dense linear systems
    slides [tex, pdf], notebook [ipynb, pdf]

05. Sparse data structures and basic linear algebra subprograms
    slides [tex, pdf], notebook [ipynb, pdf]

06. Introduction to direct methods for sparse linear systems
    slides [tex, pdf]

07. Orthogonalization and least-squares problems
    slides [tex, pdf], notebook [ipynb, pdf]

08. Basic iterative methods for linear systems
    slides [tex, pdf], notebook [ipynb, pdf]

09. Basic iterative methods for eigenvalue problems
    slides [tex, pdf]

10. Locally optimal block preconditioned conjugate gradient
    slides [tex, pdf], notebook [ipynb, pdf]

11. Arnoldi and Lanczos procedures
    slides [tex, pdf], notebook [ipynb, pdf]

12. Krylov subspace methods for linear systems
    slides [tex, pdf], notebook [ipynb, pdf]

13. Multigrid methods
    slides [tex, pdf]

14. Preconditioned iterative methods for linear systems
    slides [tex, pdf], notebook [ipynb, pdf]

15. Restarted Krylov subspace methods
    slides [tex, pdf], notebook [ipynb, pdf]

16. Elements of randomized numerical linear algebra
    slides [tex, pdf], notebook [ipynb, pdf]

17. Introduction to communication-avoiding algorithms
    slides [tex, pdf], notebook [ipynb, pdf]

18. Matrix function evaluation
    slides [tex, pdf], notebook [ipynb, pdf]

Extra notes [tex, pdf].