MATH 170A Introduction to Numerical Analysis:
Numerical Linear Algebra

Instructor

• Prof. Melvin Leok
  Office: AP&M 5763
  Email: mleok@math.ucsd.edu
  Office Hours: MW 1:00pm-1:50pm, or by appointment.

Teaching Assistant

• Joseph Reed
  Office: AP&M 5801
  Email: j2reed@math.ucsd.edu
  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.

Course Description

• Analysis of numerical methods for linear algebraic systems and least squares problems. Orthogonalization methods. Ill-conditioned problems. Eigenvalue and singular value computations.

Textbook

• Biswa Datta, Numerical Linear Algebra and Applications, Second Edition, SIAM Press, 2010.

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, least-squares)
• Fri, 11/12/2010, Chapter 8.7.3, 8.7.4 (SVD for least-squares, linear systems)
• 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, Gauss-Seidel)
• 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.

Announcements

• Midterm #1 will be in class, on Wednesday, October 20. It will cover all the material up to and including the least squares method (Chapter 8). No 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 cover 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.
• Homework #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, at 4pm.
• Homework #5 [ PDF ], includes solutions. This 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

Additional Reading

• 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.

Resources

• A free software that implements many features of MATLAB, and is mostly compatible with the MATLAB programming language is Octave. There are also other MATLAB Clones available.

Prerequisites

• MATH 20F and a good knowledge of MATLAB.

Collaboration Policy

• 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.

Email Policy

• 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 your friend.
• 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 resource.
• 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 office hours.

Academic Dishonesty: