MA/CSC 428 - Introduction to Numerical Analysis II

You can download the course information here.
More information can be found on the course Moodle page.
Reference: [Sauer] Timothy Sauer, Numerical Analysis, 2nd/3rd Edition, Pearson (ISBN 978-0-321-78367-7).

Spring 2022 Tentative Course Schedule

Week 1

  • 01/11 Lecture 1: Welcome and Course Overview; Review of Linear Algebra
    • slides on Moodle
  • 01/13 Lecture 2: Triangular Systems
    • notes on Moodle

Week 2

  • 01/18 Lecture 3: Gaussian Elimination; LU Decomposition
    • [Sauer] sections 2.1 - 2.2
    • Homework 1 posted on Moodle
  • 01/20 Lecture 4: LU Decomposition; Matrix Norms

Week 3

  • 01/25 Lecture 5: Conditioning and Error Analysis
    • [Sauer] section 2.3
  • 01/27 Lecture 6: QR Decomposition
    • [Sauer] section 4.3

** Homework 1 due Thursday

Week 4

  • 02/01 Lecture 7: Gram-Schmidt Orthogonalization
    • [Sauer] section 4.3
  • 02/03 Lecture 8: Householder Transformation
    • [Sauer] section 4.3.3

Week 5

  • 02/08 Lecture 9: Least Squares Models, Least Squares via QR Decomposition
    • [Sauer] section 4.1
  • 02/10 Lecture 10: Geometric Meaning of Least Squares Solution
    • [Sauer] section 4.1

** Homework 2 due Thursday

Week 6

  • 02/15 Lecture 11: Singular Value Decompositions I
    • [Sauer] section 12.3
  • 02/17 Lecture 12: Singular Value Decompositions II
    • [Sauer] section 12.3, 12.4

Week 7

  • 02/22 Lecture 13: SVD for least squares problems
    • See notes on Moodle
  • 02/24 Lecture 14: Eigenvalue Problems
    • [Sauer] section 12.1

** Homework 3 due Thursday

Week 8

  • 03/01 Lecture 15: Power Methods
    • [Sauer] section 12.1.1, 12.1.2
  • 03/03 Lecture 16: Inverse Power Methods
    • [Sauer] section 12.1.3

Week 9

  • 03/08 Lecture 17: QR Algorithm
    • [Sauer] section 12.2
  • 03/10 Lecture 18: Shifted QR Algorithm
    • [Sauer] section 12.2

** Homework 4 due Thursday

Week 10

  • 03/14, 03/16 Spring Break: No Class.

Week 11

  • 03/22 Lecture 19: Stationary Iteration I
    • [Sauer] section 2.5
  • 03/24 Lecture 20: Stationary Iteration II
    • [Sauer] section 2.5

Week 12

  • 03/29 Lecture 21: Krylov Methods in General
  • 03/31 Lecture 22: Arnoldi Iteration and GMRES
    • [Sauer] section 4.4

** Homework 5 due Monday

Week 13

  • 04/05 Lecture 23: Conjugate Gradient Method
    • [Sauer] section 2.6.1
  • 04/07 Lecture 24: Conjugate Gradient Method II
    • [Sauer] section 2.6.3

** Homework 6 due Thursday

Week 14

  • 04/12 Lecture 25: Numerical Optimization I - Newton’s iteration, Gradient Descent
    • [Sauer] section 13.2.1 - 13.2.2
  • 04/14 Lecture 26: Numerical Optimization II - Conjugate Gradient Search
    • [Sauer] section 13.2.3
    • Notes on Moodle

Week 15

  • 04/19 Lecture 27: Catch up
  • 04/21 Lecture 28: Review

** Homework 7 due Thursday

** 04/26 - 04/27: Reading Days

Final Exam: April 28, 2022, 12:00 pm - 2:30 pm