# 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