AMATH 584
SLN 1208, MWF 2:30-3:20, Guggenheim Hall 306
Applied Linear Algebra and Introductory Numerical Methods
Instructor:
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Professor
Loyce Adams
Guggenheim 408L
tel: 543-5077
fax: 685-1440
adams@amath.washington.edu
office hours: MWF: 1:30-2:30, T,Th: Appt.
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Teaching Assistant:
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Dominique Wiest
Guggenheim 417
tel:
fax: 685-1440
wiestd@amath.washington.edu
office hours: MW 3:30-4:30
MATLAB HELP: Email her for a time.
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Course Description
This course is an introductory graduate level course in numerical methods
designed to give engineering, mathematics, and science students the expertise
necessary to understand and use computational methods for solving scientific
problems. The emphasis is on methods for linear algebra problems (direct
methods for linear systems, linear least squares problems, algebraic
eigenvalue problems) and methods for ordinary differential equations (the
initial value problem). This course is the first in a series of three
numerical methods courses. This is a five (5) credit course.
Prerequisites
FORTRAN or C programming
ODE's (AMATH 351, MATH 307, or equivalent)
Linear Algebra (MATH 308 or equivalent)
Recommended Preparation:
Proficiency in a computing language and familiarity with UNIX.
Computer Usage:
Need access to Matlab. Math Sciences Computer Center in Thompson Hall is an option.
Computer Software:
MATLAB, LAPACK.
Laboratory Projects:
Approximately five computer projects using numerical software.
Syllabus
- 1. Numerical Approximation and Computation Errors
- (a) Truncation error
- (b) Floating point arithmetic, machine epsilon
- (c) Catastrophic cancellation
- (d) Ill-conditioning, stability
- 2. Review of Applied Linear Algebra
- (a) Change of basis, null space, range, rank
- (b) Eigendecompositions, similarity transformations
- (c) Vector norms, matrix norms
- (d) Special matrices: symmetric, orthogonal, permutation, projectors,
lower and upper triangular, tridiagonal, banded, Hessenberg, Householder
- 3. Direct Methods for Solving Dense Systems of Linear Equations
- (a) Gaussian elimination with partial pivoting
- (b) Cholesky decomposition, A=LDLT for symmetric matrices
- (c) Solution of triangular systems, multiple right hand sides
- (d) Software: LAPACK, NETLIB, MATLAB
- 4. Direct Methods for Solving Sparse Structured Systems of Linear
Equations
- (a) Tridiagonal systems
- (b) Banded systems
- (c) Block Tridiagonal
- 5. Linear Least Squares Problems
- (a) The Full Rank Case
- i. Normal equations
- ii. QR factorization approach
- (b) The Rank Deficient Case
- i. QR with pivoting
- ii. The SVD and the minimum norm solution
- (c) Software: LAPACK, NETLIB, MATLAB
- 6. Other Applications of the SVD
- (a) The null space problem
- (b) Image processing
- 7. The Algebraic Eigenvalue Problem
- (a) The Power and Inverse Power methods
- (b) QR algorithm
- (c) Lanczos techniques for sparse problems
- (d) Software: LAPACK, NETLIB, MATLAB
- 8. Systems of Nonlinear Equations
- 9. ODEs - The Initial Value Problem--(Instructor's Notes)
- (a) Issues of stability, convergence, consistency, stepsize control
- (b) Euler's method, Trapezoid method
- (c) Runge-Kutta formulas
- (d) Software: NAG, NETLIB, LSODE
Textbooks
Trefethen, L. & Bau, D. Numerical Linear
Algebra. SIAM Publishing, 1997.
Available at the University Bookstore.
Schedule and Homework
Follow links in the table below to obtain a copy of the homework in
PostScript (.ps) or 
Adobe
Acrobat (.pdf) format. You may also obtain here solutions to some of the
homework and exam problems. An item shown below in plain text is not yet
available. For additional information regarding viewing and printing the
homework and solution sets,
click here.
| Homework and Exams |
Homework Due Date |
Homework Problem Sets |
Homework Solutions |
| First day of classes |
Monday, September 29 |
| Homework#1 |
Friday, Oct 8 |
(.ps), (.pdf) |
| Homework#2 |
Wed, Oct 22nd |
(.ps), (.pdf) |
| Homework#3 |
Fri, Oct 31st |
(.ps), (.pdf),
HW 3 Matlab File: clgs.m ,
HW 3 Matlab File: mgs.m ,
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|
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| Exam I |
Wed, Nov 5 |
Exam #1
Practice Exam 1: inclass.pdf ,
Practice Exam 1: takehome.pdf ,
Exam 1: exam1.pdf ,
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| Veteran's Day |
Tuesday, November 11 |
No class |
| Homework#4 |
Fri, Nov 21 |
(.ps), (.pdf),
HW 4
Matlab File: ellipse.m
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| Thanksgiving Day |
Thursday, November 27 |
No class |
| Thanksgiving |
Friday, November 28 |
No class |
| Homework#5 |
Dec 8 |
(.ps), (.pdf)
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| Last day of classes |
Thursday, December 11 |
| Final-Part 1 |
Due Dec 18, 9am |
(.ps), (.pdf)
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| Final-Part 2 |
Due Dec 18, 9am |
(.ps), (.pdf)
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Grading
Computer projects and homework: 50%, midterm: 25%, final: 25%.
You may view your homework and exam
grades on-line.
Before doing so for the first time, you must
request
a password. Please note this change to our system: Your student
ID number should be entered including any leading zeros
(e.g. 0012345).
Tutorials
- Matlab Plotting Tutorial.ps,
- Matlab Plotting Tutorial.pdf
- This is a brief tutorial on plotting in Matlab.
- NAG Fortran Library Routine Document D02EJF.ps,
- NAG Fortran Library Routine Document D02EJF.pdf
- This is the documentation for NAG Fortran Library Routine Document D02EJF.