Advanced Numerical Linear Algebra (Math 243M), Spring 2017, San Jose State University

MacQuarrie Hall 224, TuTh 4:30-5:45pm

Instructor: Plamen Koev

Office: MacQuarrie 312

Office hours: TuTh 3-4:30

E-mail: firstname dot lastname at

Web page:


Syllabus: Advanced topics in numerical linear algebra. Topics covered:

  1. Matrix-vector and Matrix-Matrix products
  2. Orthogonal matrices, norms of vectors and matrices
  3. The singular value decomposition
  4. QR decomposition
  5. Givens rotations and Householder reflectors
  6. Least Squares Problems
  7. Floating point arithmetic
  8. Accuracy, Stability and Conditioning
  9. Backward Stability
  10. Conditioning of Least Squares Problems
  11. Gaussian Elimination
  12. Cholesky Factorization
  13. Eigenvalue Problems
  14. Hessenberg reduction
  15. QR Iteration
  16. Jacobi algorithm
  17. Bisection and divide-and-conquer algorithms
  18. SVD algorithms, LR interation, dqds
  19. Iterative algorithms, Arnoldi
  20. Lanczos algorithm
  21. Conjugate gradients
Prerequisite: Math 143C or Math 143M or instructor consent.

Textbooks: Applied Numerical Linear Algebra by James Demmel, 1997. Numerical Linear Algebra by Lloyd Trefethen and David Bau, SIAM Press, 1997.

Software: MATLAB (or its free clone, OCTAVE) will be required. MATLAB access can be gained by getting a math department account, by using the machines in Engineering or Physics (if you are taking engineering or physics courses), or by buying a copy of Student MATLAB.

Workload expectations: You are expected to spend 9 hours per week on this course, which includes class attendance, studying, homework, etc.

Course Objectives: Upon successful completion of this course, students will be able to understand the commonly used algorithms for the topics of the course; to be able to compare these algorithms in terms of efficiency, accuracy and reliability. To understand the derivations of the algorithms and the major theoretical results related to the algorithms, including their proofs. To develop the skills required to investigate a specific topic in depth and present the results of the investigation orally and in writing.

Outcome Assessment: A midterm worth 20%, a project worth 20%, a comprehensive final exam worth 40% and homework worth 20%. You must plan to take the exams at their scheduled times. Exceptions are rarely granted and only in documented circumstances in accordance with University policy.
No calculators, computers, or cellphones will be permitted during exams.

Curve: A/B/C/D for 90/80/70/60 with +/- for the upper/lower third of the range. For example, 81 is a B-.

Homework: You only need to complete 80% of the homework assignments correctly in order to obtain full credit. Thus, no late homework will be accepted! You are free to collaborate on homework, but everyone must turn in their own solutions.

Academic integrity. Your commitment to learning (as shown by your enrollment at SJSU) and the university's Academic Integrity Policy require you to be honest in all of your academic course work. Faculty are required to report all infractions to the Office of Judicial Affairs. Cheating, in particular, will result in an automatic F in the course. (See:

Disabilities. If you need course adaptations or accommodations due to a disability, or if you need special arrangements in case the building must be evacuated, please make an appointment with me as soon as possible, or see me during office hours. Presidential Directive 97-03 requires that students with disabilities register with the Disability Resources Center to establish a record of their disability.

Tutoring. Peer tutoring in calculus is available to all SJSU students, free of charge, at the Learning Assistance Resource Center, in Room 600 of the Student Services Center. See or call x4-2587 for more information.