Numerical Methods

• Instructor: Chih-Jen Lin, Room 413, CSIE building.
  The best way to contact me is via e-mails.
• TAs:
  Jui-Yang Hsia, email: r08922195 at ntu.edu.tw
  Sheng-Wei Chen, email: d09944003 at ntu.edu.tw
  TA hours: CSIE R530 Tue. 14:00 ~ 15:00



Your HW/exam scores

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

  No class on June 15 because we will finish all slides on June 8. The final exam is still on June 22.
  

  Place: room 105, 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 ( video )
• 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

• HW1, due on March 16
• HW2, due on March 30
• HW3, due on April 13
• HW4, due on April 27
• HW5, due on May 11
• HW6, due on May 25
• HW7, due on June 8
• HW8, due on June 22

Exams

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 30 (week 6) Solutions
• Midterm 2: May 11 (week 12) Solutions
• Final: June 22 (week 18) Solutions
  

For midterms, discussions will be in the following week. The discussion for the final exam will be at 12 pm 6/25 Fri (online).

Grading

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

FAQ

Issues related to COVID-19

• According to school's regulation, all students must wear masks
• If the covid situation becomes serious, we will move the course online.
• If you are sick, please do not come to the class.