Numerical Methods for Simulation, Optimization, and Control

MAE 290A

Fall 2013

Lectures

09:00-09:50AM, MWF at CSB 002 PETER 104

Instructor

Mauricio de Oliveira, first name at ucsd dot edu

Office hours

10:00-11:00AM Wed at EBU I 1602.

TA

Ed Pogue, e last name at ucsd dot edu

Office hours

02:00-03:00PM Th at EBU I 1603.

Textbook

The main reference material for this course is the electronic book Numerical Renaissance: simulation, optimization, & control by Thomas Bewley.

The book can be read or downloaded here.

We will cover the first 4 Chapters then some select sections, time permitting. I will shuffle much of the material as we go through the text.

Other Useful References

• Matrix Analysis, Roger Horn & Charles Johnson, Cambridge University Press, 1985
• Matrix Analysis for Scientists & Engineers, Alan Laub, SIAM, 2005
• Matrix Computations, Gene Golub & Charles Van Loan, The John Hopkins University Press, Third Edition, 1996

Matlab

We will make extensive use of Matlab for computations, so it is important that you have access to a computer with Matlab.

You will need Matlab to complete some of the assignments.

In this class, almost everything you need can be done with the Student Version of Matlab (100$ at the bookstore) as well as with the free Matlab clone Octave.

Matlab Files

• Matrix/Vector Multiplication
• LU Decomposition
• LU Decomposition - in place
• Loss of Precision in LU Decomposition
• LU Decomposition with Partial Pivoting
• LU Decomposition - Near zero pivot
• LU Decomposition - Singular matrix
• LU Decomposition - Worst case growth
• LU Decomposition with Complete Pivoting
• LU Decomposition - Singular matrix
• LU Decomposition - Growth
• LDL Decomposition
• Cholesky Decomposition
• Matlab Slash
• Gram-Schmidt
• Modified Gram-Schmidt

Exams and Assignments

Homework

1. Homework #1
   Due on: 10/18/2013
   solution
2. Homework #2
   Due on: WILL NOT BE GRADED
   solution
   Beware that Ed uses A = P L U and A = P L U Q^T for his LU with partial and complete pivoting!
   In class I used P A Q = L U and P A Q = L U which is more standard.
3. Homework #3
   Due on: 11/15/2013 11/18/2013
   solution
4. Homework #4
   Due on: 11/29/2013 12/03/2013
   solution

Midterm

• 11/01/2013, in class
  Exam starts at 8:30 AM
  solution

Final

• 12/11/2013, 08:00-10:59AM, PETER 104
  solution

Grade

GRADE = 0.3 * HOMEWORK + 0.3 * MIDTERM + 0.4 * FINAL

Past Exams

Here is a link to some past exams with solutions.