ScheduleΒΆ

  1. Preliminaries ~ 2 weeks

    Lecture 1, 2016-01-20 Read: The syllabus.

Lecture 2, 2016-01-22 Read: An undergraduate text on linear algebra, GvL: 1.1, 1.3, 2.1. D: 1.1, 1.2, 1.3, 2.3. TB: 1, 2.

  • Where does \(Ax=b\) come from?
  • How do we solve \(Ax=b\)?
  • How do we actually solve \(Ax=b\)?
  • LU by matrix multiplications.
  • Block operations.

Lecture 3, 2016-01-25 Read: GvL 1! D: 2.6. ASNA 3.1, 3.5, (23). Also read the pdf from this repository.

  • Briefly on computers.
  • BLAS and its history.
  • Matrix multiplication (time permitting see also homework 2.).

Lecture 4, 2016-01-27 Read: GvL: 2.2, 2.3, 2.6, 2.7! D: 1.5, 1.7 TB: 3, 13. ASNA: 1, 2.

  • Finite precision.
  • Floating point arithmetic.
  • Absolute and relative errors.
  • The standard model.
  • The residual and what it tells us about the accuracy in the solution.
  1. Gauss Elimination Basics ~ 2 weeks

    Lecture 5, 2016-01-29 Read: GvL: 3.1.

    • Catch up.
    • Triangular systems.

    Lecture 6, 2016-02-01 Read: GvL: 3.2

    • LU.

    Lecture 7, 2016-02-03 Read: GvL: 3.3

    • Roundoff in GE.
    • Growth factor.

    Lecture 8, 2016-02-05 Read: GvL: 3.4.

    • Pivoting.
    • Implementation.
    • Error analysis.

    Lecture 9, 2016-02-08 Read: GvL: 2.6. D: 2.2. TB: 12, 13, 14. ASNA: 7.

    • Error analysis.
    • Perturbation theory.
    • The condition number.

    Lecture 10, 2016-02-10 Read: GvL: 2.6. D: 2.2. TB: 12, 13, 14. ASNA: 7.

    • Perturbation theory.
    • The condition number.
    • Examples.
    • Catch up.

    Lecture 11, 2016-02-12 Read: GvL: 3.5

    • Iterative refinement.
    • Computing the inverse.
    • Catch up.
  2. Gauss Elimination Special Systems ~ 2 weeks

    Lecture 12, 2016-02-15

    • Symmetric systems.

    Lecture 13, 2016-02-17

    • Banded systems.

    Lecture 14, 2016-02-19

    • Sparse systems.
    • Storage.

    Lecture 15, 2016-02-22

    • Sparse systems.
    • Reordering algorithms.

    Lecture 16, 2016-02-24

    • Block algorithms.
    • Parallel considerations

    Lecture 17, 2016-02-26

    Lecture 18, 2016-02-29

    Lecture 19, 2016-03-02

  3. Linear Least Squares ~ 2 weeks

    Lecture 20, 2016-03-04

    • Basics.
    • Why?
    • Normal equations.
    • Ways to derive NE.

    Lecture 21, 2016-03-07

    Lecture 22, 2016-03-09

    Lecture 23, 2016-03-11

    Lecture 24, 2016-03-21

    Lecture 25, 2016-03-23

  4. Iterative Methods ~ 3 weeks

    Lecture 26, 2016-03-25

    Lecture 27, 2016-03-28

    Lecture 28, 2016-03-30

    Lecture 29, 2016-04-01

    Lecture 30, 2016-04-04

    Lecture 31, 2016-04-06

    Lecture 32, 2016-04-08

    Lecture 33, 2016-04-11

    Lecture 34, 2016-04-13

  5. Eigenvalue Problems ~ 3 weeks

    Lecture 35, 2016-04-15

    Lecture 36, 2016-04-18

    Lecture 37, 2016-04-20

    Lecture 38, 2016-04-22

    Lecture 39, 2016-04-25

    Lecture 40, 2016-04-27

    Lecture 41, 2016-04-29

    Lecture 42, 2016-05-02

    Lecture 43, 2016-05-04

    Lecture 44, 2016-05-06