Numerical Analysis 1 | MA | Course

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

 

 

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