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MATH 170A Introduction to Numerical Analysis:
Numerical Linear Algebra
MWF 3:00pm - 3:50pm, PETER 102.
- Prof. Melvin Leok
Office: AP&M 5763
Office Hours: MW 1:00pm-1:50pm, or by appointment.
- Joseph Reed
Office: AP&M 5801
Section: Th 4:00pm - 4:50pm, and 5:00pm - 5:50pm, WLH 2115
Office Hours: T 2pm - 3pm, W 2pm - 3pm, Th 10am - 11am, Th 2:30pm -
3:30pm, APM 5801.
Analysis of numerical methods for linear algebraic systems and least
squares problems. Orthogonalization methods. Ill-conditioned problems.
Eigenvalue and singular value computations.
Sections to be covered:
- Fri, 9/24/2010, Chapter 1
- Mon, 9/27/2010, Chapter 3.1-3.3
- Wed, 9/29/2010, Chapter 3.4-3.5
- Fri, 10/1/2010, Chapter 4.1-4.2
- Mon, 10/4/2010, Chapter 5.1
- Wed, 10/6/2010, Chapter 5.2.1
- Fri, 10/8/2010, Chapter 5.2.2-5.2.3
- Mon, 10/11/2010, Chapter 5.2.4
- Wed, 10/13/2010, Chapter 8.1-8.4
- Fri, 10/15/2010, Chapter 7.1-7.2
- Mon, 10/18/2010, Review Session
- Wed, 10/20/2010, Midterm 1
- Fri, 10/22/2010, Chapter 7.2 (QR Factorization)
- Mon, 10/25/2010, Chapter 7.6 (Solving Ax=b using QR)
- Wed, 10/27/2010, Chapter 8.7.2 (Using QR to do least squares)
- Fri, 10/29/2010, Chapter 7.1, 7.5 (Revisited definition of reduced QR
factorization, and using Gram-Schmidt to compute reduced QR)
- Mon, 11/1/2010, Chapter 7.5 (CGS and MGS methods)
- Wed, 11/3/2010, Chapter 7.7 (Projections using QR)
- Fri, 11/5/2010, Chapter 7.8 (Singular Value Decompositions)
- Mon, 11/8/2010, Chapter 7.8.4, 7.8.7 (Interpretation of SVD,
Applications to Rank, Norms, etc.))
- Wed, 11/10/2010, Chapter 7.8.10, 8.7.3 (SVD applied to projections,
- Fri, 11/12/2010, Chapter 8.7.3, 8.7.4 (SVD for least-squares,
- Mon, 11/15/2010, Chapter 10.3.5, 10.3.6 (Computing the SVD)
- Wed, 11/17/2010, Review Session
- Fri, 11/19/2010, Midterm 2
- Mon, 11/22/2010, Chapter 12.1, 12.2 (Iterative methods, Jacobi,
- Wed, 11/24/2010, Discussed Newton Fractals as an example of domains
of convergence of iterative methods, showed a MATLAB code which uses
vectorization to compute these. See this website
for the code.
- Midterm #1 will be in class, on Wednesday, October 20. It will
all the material up to and including the least squares method (Chapter 8).
calculators, or textbooks are allowed, but you are permitted one sheet of
notes (front and back, letter sized page).
For least squares, review Section 8.2 (page 238), 8.4 (page 242), and
Exercises 8.4 (page 271).
- Midterm #2 [ Solutions ]
will be in class, on Friday, November 19. It will
all the material involving QR, reduced QR, and their applications. No textbooks are allowed, but you are permitted one sheet of
notes (front and back, letter sized page). You are allowed to
use a calculator for elementary operations, but it is
absolutely critical that you show your work.
#1 [ PDF | Solutions ], due Monday,
10/11/2010, at 4pm.
- Homework #2 [ PDF | Solutions ], due Friday,
10/15/2010, at 4pm.
- Project #1 [ PDF ],
due Monday, 10/25/2010, at 4pm.
- Homework #3 [ PDF | Solutions ], due Friday,
11/5/2010, at 4pm.
- Project #2 [ PDF ],
due Monday, 11/15/2010, at 4pm.
- Homework #4/Project #3 [ PDF ], due Wednesday, 12/1/2010,
- Homework #5 [ PDF ], includes solutions.
is for practice on iterative methods, and does not need to be turned in.
- The final exam will be on Friday, December 10, 2010, from 3:00pm to
6:00pm. It will be comprehensive, and you are allowed two sheets of notes
(front and back).
- Course Handout
- Introduction to MATLAB
- Cleve Moler, Numerical Computing with MATLAB, SIAM, 2004.
- Endre Süli and David Mayers, An
Introduction to Numerical Analysis, Cambridge, 2003.
- Brian Bradie, A
Friendly Introduction to Numerical Analysis, Prentice Hall, 2005.
- Eugene Isaacson and Herbert Keller, Analysis
of Numerical Methods, Dover, 1994.
- Richard Burden and Douglas Faires, Numerical
Analysis, 8th Edition, Brooks/Cole, 2004.
- A free software that implements many features of MATLAB, and is mostly
compatible with the MATLAB programming language is Octave. There are also
- MATH 20F and a good knowledge of MATLAB.
- Homework is an essential part of advanced mathematics courses. Most
students will find that some problems will require repeated and persistent
effort to solve. This process is an integral component of developing a
mastery of the material presented, and students who do not dedicate the
necessary time and effort towards this will compromise their performance
in the exams in this course, and their ability to apply this material in
their subsequent work.
- A student may after working conscientiously on a problem for over 30
minutes, consult with other current MATH 170A students to develop and
clarify their approach to the problem. The written solution should however
be an independent and individual effort that reflects the student's
understanding of the problem and its solution.
- As a general guide, a student should be able to independently
reproduce any solution that is submitted as homework. Copying of solutions
is not permitted and will be considered a violation of these guidelines.
- I will not respond to emails which are composed in an unprofessional
manner, or which violates basic email etiquette. Think professional
business letter to a potential employer, as opposed to a text message to
- Before sending an email inquiry, please carefully review the syllabus
and course website to ensure that your question has not been addressed
there. Questions that have been addressed in the syllabus or on the course
website will receive responses that redirect you back to the appropriate
- I do not offer immediate round the clock technical support, please
plan ahead accordingly.
- I will try to respond to emails within 36 hours during the week, and
within 72 hours during the weekend.
- Emailed questions should primarily be limited to clarification of the
homework questions, and I will defer questions that require more
substantial responses, in particular programming questions, to my
Academic dishonesty is considered a serious offense at UCSD. Students
caught cheating will face an administrative sanction which may include
suspension or expulsion from the university. It is in your best interest
to maintain your integrity. Suspected violations will be investigated in
accordance with university
statute and referred to the academic