Welcome to the CSE/Math 447, Numerical Analysis II: Numerical Linear Algebra, home page. You're probably here for information, so let's start with the vital statistics of the course.

### Numerical Linear Algebra Resources

• Course Description So what is this "numerical linear algebra" all about?
• Lloyd N. Trefethen. Home Page of one of our textbook's authors.
• Maxims Words of wisdom from one of our authors.
• Netlib A huge repository of mathematical software, papers, and databases.
• Maple Math Site Has lots of information about the Maple software which is available on math department computers.
• Wikipedia and OR Lots of information (of varying quality!) about many subjects.
• SIAM Home Page Every serious student of applied mathematics should consider joining the Society for Industrial and Applied Mathematics!
As you know, a staggering amount of information can be found on the web. Of course, some of it helps, some confuses, and some is downright wrong -- caveat emptor! Go to your favorite search engine and try searching on "numerical linear algebra". See how many web pages you hit and visit a few interesting looking sites.

## Notes and FAQ

8/12/08:(Just to get the FAQ started) About significant digits...
I've been asked to explain what "significant digits of an approximation" to a (nonzero) number means. There are several interpretations that one commonly sees. The "absolute" definition, which is perhaps more intuitive, goes as follows: to get the number of significant digits, first *subtract* (rather than just looking at the numbers) the two (may as well be larger - smaller), then find the position of the leading digit of the error relative to the position of leading digit of the exact answer. If the difference in that position is less than 5, then number of significant digits is one less than the difference, else two less.

For example if 3.14 and 3.15 are used to approximate 3.14159, calculate 3.14159 - 3.14 = 0.00159 and 3.15 - 3.14159 = 0.00841. Notice I put a zero in front of the decimal to start counting from the right position. There is a nonzero digit at the 4th position with each approximation, counting from the (base 10) position of the leading digit of 3.14159. The size of this digit is at most 5 in the first case, so this approximation has 3 significant digits. In the second case, the digit is larger than 5, so the approximation only has 2 significant digits.

The "relative" definition is usually preferred in numerical analysis and it goes as follows: if xapprox is used to approximate xtrue, the number of significant digits is largest integer n such that the relative error, |(xapprox-xtrue)/xtrue)| is no larger than 5x10^(-n-1). In our previous example the relevant quotients are 0.000506 and 0.002677, respectively. The best bound in both cases is 5x10^(-3). Thus, this definition will give only 2 significant digits in both cases. In general, the "relative" definition is stingier than the "absolute" one. Hope this helps.

### Class Policy Statement

Course: CSE/Math 447, Numerical Analysis II: Numerical Linear Algebra

Place/Time: AvH 12, 3:30-4:45 TR, Fall 2008

Preq: CSE/Math 340, Math 221 and 314 or equivalent, or permission.

Objectives: To help students achieve competence in the following areas:

• Understanding of basic theory of numerical linear algebra.
• Knowledge of the most common algorithms and their applicability.
• Stability and efficiency (complexity) of these algorithms.
• Implementation of and experiments with the algorithms (mainly via Matlab platform).
Instructor: Dr. Thomas Shores

Telephone: Office 472-7233   Home 489-0560

Email: tshores1@math.unl.edu

Office Hours: Monday 2:00-4:00, Tuesday 13:00-15:00, Thursday 11:00-13:00, Friday 9:00-10:30, and by appointment. Office: 229 AvH
Note: Circumstances may necessitate occassional changes in office hours. Consult the course home page for the most current times.

Class Attendance: Is required. If absent, it is incumbent upon the student to determine what has been missed as soon as possible. It is advisable to consult with the instructor.

Homework/Projects: Homework will be assigned in class and collected according to the syllabus collection dates. All homework assigned one week or more before the collection date is due on that date. Most of the homework assignment problems will be graded in detail for homework points. It is strictly forbidden to copy someone else's homework, though some discussion with other students is allowed. For some of the more substantial exercises I will allow teams of two to turn in a single solution with clear attribution of partnership. The official programming language for this course is Matlab. Prior experience in Matlab is not required. Students will be given an account in the Mathematics Computer Lab for computer related exercises and can obtain written lab instructions in the lab itself. Current information about the course will be available on the web (via Blackboard or my home page). Using the web is strongly recommended for keeping track of due dates for homework collections and other current activities in the course.

Reading Assignment: Read the sections of the texts as, or before, they are covered in class lectures. This is a standing assignment throughout the semester.

Grade: A midterm will be given outside of class meeting time and will account for 130 points. The final exam will count 150 points. Exams may have a take home component. All in-class exams are closed book. Homework will count 220 points. The final grade will be based on these 500 points.

Final Exam: Will be comprehensive. To be given on Monday, December 15, 8:30 - 10:30 pm in AvH 12.

Grades of "I", "W" or "P": These grades will be given in strict accordance with University policy. (See any Schedule of Classes for the relevant information and dates.)

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