AMS 526: Numerical Analysis I (Numerical Linear Algebra)
Fall 2012
Time: Monday & Wednesday 4:00 pm - 5:20 pm
Location: Physics P122
Lecture schedule (tentative)

[ Course Description | Course Outline | Course Policy | Homework and Tests | References | University Policy ]

Course Description (back to top)

Direct and iterative methods for solving simultaneous linear equations. Matrix factorization, conditioning, stability, sparsity, and efficiency. Computation of eigenvalues and eigenvectors. Singular value decomposition.

Required Textbook

• David S. Watkins, Fundamentals of Matrix Computations, 3rd edition, Wiley 2010, ISBN 978-0-470-52833-4.

Prerequisite/Co-requisite

• AMS 510 (linear algebra portion) or equivalent undergraduate-level linear algebra course. Familiarity of the following concepts is assumed: Vector spaces, Gaussian elimination, Gram-Schmidt orthogonalization, and eigenvalues/eigenvectors.
• AMS 595 (co-requisite for students without programming experience in C).

Course Outline (back to top)

Outline

• Gaussian elimination and its variants (2.5 weeks)
• Sensitivity of linear systems (2.5 weeks)
• Linear least squares problem (1.5 weeks)
• Singular value decomposition (1.5 weeks)
• Eigenvalues and eigenvectors (3 weeks)
• Iterative methods for linear systems (2 weeks)

Course Policy (back to top)

Assignments

Homework assignments are due in class typically two weeks after they are assigned. You are allowed to discuss course materials and homework problems in small groups, but limited to discussion of general ideas only. You must write your solutions completely independently. Under no circumstances may you copy solutions from any source, including but not limited to other students solutions, official solutions distributed in past terms, and solutions from courses taught at other universities. Violation of these rules may result in disciplinary actions.

Exams

The exams (including two tests and the final exam) are closed-book, but you are allowed to bring a single-sided, one-page, letter-size cheat sheet, which you must prepare by yourself.

Attendance

All students are expected to attend all the lectures and exams.

Grading

• Assignments: 30%

• Two tests: 40%

• Final exam: 30%

Homework and Sample Tests (back to top)

For the computing assignments, you are encouraged to use the Linux machines in the Mathlab SINC Site at Math Tower S-235. You can remotely log onto the Linux computer compute.mathlab.sunysb.edu using ssh. Before you can login, you may need to go to Math Tower S-235 to activate your account. You may use your own computer if it runs a UNIX system (such as Linux or Mac OS X), has a C compiler (such as gcc) and debugger (such as gdb and ddd), and has octave, gnuplot, and gv (for plotting).

You are encouraged to typeset your homework solutions using LaTeX or using LyX (a very easy-to-use document processor, using LaTeX in the backend). (However, Microsoft Word alike are not recommended because of the equations.) Hand-written homework is due in class on the due date. Homework typeset using LaTeX or LyX is due at 11:59pm on the due date, through email submission of the PDF file to the TA.

All programming part of the homework are also due at 11:59pm on the due date, through email submission of the source code and the report to the TA.

Note: The username and password of the sample solutions can be found on the Blackboard.

Assignments

• Homework #1 (due 09/12) LyX template file and code template; sample solution
  
• Homework #2 (due 09/26; extended to 09/28) LyX template file and code template; sample solution
• Homework #3 (due 10/10; extended to 10/12) LyX template file; sample solution
• Homework #4 (due 10/24) and code template and sample solution
• Homework #5 (due 11/19) and code template and sample solution
• Homework #6 (due 12/05; extended to 12/07) and sample solution

Sample Tests

• Sample test for midterm #1; sample solution
• Sample test for midterm #2; sample solution
• Sample test for final exam; sample solution

References (back to top)

References on Undergraduate-Level Linear Algebra

The following is an excellent text for reviewing fundamental concepts and some applications of linear algebra.

• Gilbert Strang, Linear Algebra and Its Applications, 4th Edition, Brooks Cole, 2006.
  

Other References on Numerical Linear Algebra

The following books are graduate-level textbooks on numerical linear algebra, similar to the main textbook for this course.

• Gene H. Golub and Charles F. Van Loan, Matrix Computations, 3rd edition, John Hopkins University Press, 1996, ISBN 0-8018-5414-8.
• Lloyd N. Trefethen and D. Bau III, Numerical Linear Algebra, SIAM, 1997.
• James W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.

References on Iterative Methods and Multigrid Methods

The following books are for additional readings on iterative methods and multigrid methods, which are increasingly important but not covered in this course due to time constraint.

• Anne Greenbaum, Iterative Methods for Solving Linear Systems, SIAM, 1997.
  
• Yousef Saad, Iterative Methods for Sparse Linear Systems, SIAM, 2003.
• William L. Briggs, Van Emden Henson, Steve F. McCormick, A Multigrid Tutorial, 2nd edition, SIAM, 2000.

References on C Programming

If you want to purchase a C book, a classical one is

• B.W. Kernighan, D.M. Ritchie, C Programming Language (2nd edition). Prentice Hall, 1988.

There are some free online books linked at this "C Programming Language" page. Among these, the following book might be most appropriate.

• M. Banahan, D. Brady and M. Doran, The C Book, second edition, Addison Wesley, 1991.

Another good starting point is the community-written C book is

• C Programming, Wikibooks

References on Technical Writing

Policies and Academic Integrity (back to top)

Americans with Disabilities Act

Academic Integrity

Critical Incident Management