Brief Information

• Name : Numerical Analysis 1
• Lecturer : Lee Jin-woo
• Semester : 2014 Fall
• Course : BS, Mathematics
• Textbook
  1. Sauer, T. (2011)?Numerical Analysis. 2nd Ed. Pearson
  2. Klein, P., N. (2013) Coding the Matrix: Linear Algebra through Applications to Computer Science. 1st Ed.? Newtonian Press
• Syllabus [link]

Trace lectures

Listing themes I learned in the lecture in time order.

• Least squares and the normal equations
• Lagrange interpolation
• Newton’s divided differences
• [Midterm-exam]
• Gaussian elimination | implement it in Python
• LU factorization?| implement it in Python
• PA=LU factorization?| implement it in Python
• Fixed point iteration?| implement it in Python?and visualizing
• Cubic splines
• QR factorization and least squares
  • using Gram-Schmidt orthogonalization and least squares
  • using Householder reflectors
• Nonlinear least squares using Gauss-Newton method
• Conjugate gradient method

Assignments

1. Check the results of Task 0.5.1 ~?0.5.20 in Coding the Matrix?and report them.?(Practice Python)
2. Task 0.5.21 ~?0.6.4 in?Coding the Matrix?(Practice Python)
3. Task 0.6.5 ~?0.6.8?in?Coding the Matrix?(Practice Python)
4. Task 0.8.1 ~ 0.8.5?in Coding the matrix?(Practice Python)
5. Example 4.8 ~ 4.11?in Numerical Analysis?(Practice least squares algorithm using MATLAB)
6. Task 1.7.1 ~ 9?in Coding the Matrix
7. Implement vec.py?in Coding the Matrix. (Implement a vector class object)
8. Implement Newton Divided Difference formula?using Python and report results.
9. Project : Conjugate gradient method. Teach it, implement it in Python, and find its examples in reality. I chose the implementation.

Summarize?themes

• Basics of Python programming language
• At least squares