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Description: The aim of this
course is to introduce the essential ideas of numerical
linear algebra, to describe some of the important
algorithms in the subject, and to possibly offer a
glimpse of some of the current research problems. Matlab
will be the scientific programming language for this
course. Assignments may involve a fair amount of
scientific programming in matlab together with more
classical exercises
Prerequisite: - Ma 1abc, Ma
2ab, ACM 95(abc). Students should be comfortable with
linear algebra (undergraduate level). Some programming
experience or some willingless to learn. Prior
knowledge of matlab not required.
Syllabus:
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- Introduction to numerical computation
- Direct methods for linear systems
- QR decompositions and Least Squares problems
- Eigenvalue and eigenvector computations
- Iterative methods for large linear systems
and eigenvalue problems
- Stability and conditioning
The course will also develop applications in
inverse problems, data fitting, optimization and other
areas.
Textbooks:
- Numerical Linear Algebra by LLoyd N. Trefethen and David
Bau, III, SIAM (required)
- Applied Numerical Linear Algebra by James W. Demmel, SIAM
(optional)
- Matrix Computations by Gene H. Golub and Charles F. Van Loan, The
Johns Hopkins University Press, 3rd edition (optional)
- Introduction to Linear Algebra
by Gilbert Strang, Wellesley-Cambridge Press, 3rd edition (optional)
Handouts: I will do my best to
post online all the handouts given in class. By the way,
Sheila Shull (217 Firestone) is a person you can contact
at any time (between 9:30am and 5pm) if you need
administrative information. Her phone number is
626-395-4560.
Teaching
Assistant and Office Hours:
Svitlana Vyetrenko, TBA, 322 Guggenheim
svitlana@acm.caltech.edu
Grading:
Homework assignments: 60%
Homework will generally be distributed on Wednesdays and
due in class the following Wednesday.
There will be about 5 assignments, and your
lowest score will be dropped in the final grade.
Late homeworks will NOT be accepted for grading
(medical emergencies excepted with proof).
Final exam: 40%. There will be a
take-home final exam.
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