Numerical Methods

Instructor: Chih-Jen Lin, Room 413, CSIE building.
The best way to contact me is via e-mails.
TAs:
??, email: at ntu.edu.tw
TA hours: ??

Your HW/exam scores

Time: Monday 10:20-13:00
We will do two 10-minute breaks at around 11:10am and 12:10pm. The class ends at 1pm.

Place: room ??, CSIE building
Textbook: no
References:
- What Every Computer Scientist Should Know About Floating-Point Arithmetic David Goldberg, ACM Computing Surveys, 1991.
- Matrix computation, Fourth edition, Golub and Van Loan, Johns Hopkins Univ. Press, 2012. This is a very good book. I do recommend you to buy a copy.
- A practical introduction to Matlab by Mark S. Gockenbach
FAQ of this course is here
We will pre-record all lectures and broadcast them in the class. In the class I will give additional comments while the video is being played.

Course Outline

Floating point operations
Basic Numerical Methods
Numerical linear algebra
Interpolation and approximation

We will particularly focus on numerical linear algebra.

Slides (in pdf) and recordings

Course information
Floating-point systems
- Floating-point basics ( part 1: slides video )
- Guard digits ( part 1: slides video part 2: slides video )
- Cancellation ( part 1: slides video )
- IEEE standard ( part 1: slides video part 2: slides video part 3: slides video )
- Trap handler ( part 1: slides video part 2: slides video )
- Real example ( part 1: slides video )
Direct methods for linear systems
- LU factorization ( part 1: slides video part 2: slides video part 3: slides video )
- Cholesky factorization ( part 1: slides video part 2: slides video )
- Condition of matrices ( part 1: slides video )
BLAS
- Basic ( part 1: slides video )
- Optimized BLAS ( part 1: slides video part 2: slides video )
Iterative methods for linear systems
- Matrix storage ( part 1: slides video )
- Iterative methods ( part 1: slides video part 2: slides video )
- Conjugate gradient methods ( part 1: slides video part 2: slides video part 3: slides video part 4: slides video )
Nonlinear equations
- One variable ( part 1: slides video part 2: slides video part 3: slides video )
Approximation
- Spline ( part 1: slides video part 2: slides video )
- Regression ( part 1: slides video part 2: slides video )
Fast Fourier Transformation
- Basic ( part 1: slides video part 2: slides video part 3: slides video part 4: slides video )
- Fast Fourier Transformation ( part 1: slides video part 2: slides video part 3: slides video )

Homework

Roughly once every two weeks. Please write your homework/reports in English. Every submission after the deadline will get zero points. See FAQ about how to submit your homework.

Exams

You can bring notes (and other printed materials). Electronic devices are not allowed.

For each exam, only materials after the previous exam are covered. They may not be exactly the same as the previous years due to the teaching schedule.

Midterm 1: March 21 (week 6)
Midterm 2: April 25 (week 11)
Final: May 30 (week 16)

(Sample exam questions: 1, 2, 3)

For midterms, discussions will be in the following week. The discussion for the final exam will be at ??

Grading

30% homework, 70% Exam or 25% homework, 75% Exam (tentative)

Some (usually 10%) may fail if they don't work hard.

FAQ

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