1 Course Description

Catalog Description

Algorithms and software for fundamental problems in scientific computing. Topics: properties of floating point arithmetic, linear systems of equations, matrix factorizations, stability of algorithms, conditioning of problems, least-squares problems, eigenvalue computations, numerical integration and differentiation, nonlinear equations, iterative solution of linear systems.

1.1 Instructors

Mr. Thomas Kennedy & Dr. Nikos Chrisochoides

1.1.1 Office Hours

1.3 Meeting Times & Delivery Method

2 Basic Course Information

2.1 Reference Texts

Class notes are available on Canvas and the course site. Supplemental texts are optional:

1. (Optional) Elementary Numerical Analysis: An Algorithmic Approach, by Samuel Daniel Conte, Carl De Boor

2. (Optional) Numerical Analysis: An Introduction, By Walter Gautschi.

3. (Optional) Data Structures and Algorithms in Python Book by Michael H. Goldwasser, Michael T. Goodrich, and Roberto Tamassia

4. (Optional) Advanced Calculus: Second Edition by David V. Widder

3 Course Policies

3.1 Class Attendance

During lectures, we will be covering material from my notes. Lecture will also consist of the exploration of several real world problems not covered in any book. I may assign (or announce through Canvas) a reading assignment or thinking assignment at the end of each lecture.

You are responsible for the contents of all lectures. I expect you to attend class and to arrive on time. If you must miss a class, you are responsible for all material (e.g., lecture and assignments). I expect you to watch the recorded lecture within 24 hours.

3.2 Due Dates & Late Submissions

I do not accept late work. Exceptions to this and other grading policies will be made only in situations of unusual and unforeseeable circumstances beyond your control, and such arrangements must be made prior to the due date in any situations where the conflict is foreseeable.

3.3 Classroom Conduct

Please be respectful of your classmates and instructor by minimizing distractions during class. Cell phones must be turned off during class.

3.4 Academic Integrity

3.5 Submission (Written Exercises)

All written exercises must be submitted through Canvas in PDF format. Each such submission must take the form of a single multi-page PDF document. Failure to follow these requirements will result in a zero.

3.6 Submission (Programming Exercises)

All programming exercises (e.g., Machine Assignments) must be submitted as a single zipfile (zip) or tarball (tar.gz, tar, or tgz). Unless explicitly stated in the prompt, other formats will not be accepted. Each submission must include:

3.6.1 Permitted Languages

You may used any combination of C, C++, Java, Python (3.7+), and Rust. All other languages must be discussed with the instructor before assignment/project submission.

Extra consideration will be given to novel solutions (e.g., those written in a functional language).

3.7 Computer Accounts

Students will need an account on the CS Dept. Linux network to participate in this class. This account is unrelated to any University-wide account you may have from ODU’s Information Technology Services (ITS).

4 Grading ³

Final grades will be computed using the following weights:

Final course grades will be assigned based on the standard 10-point scale ¹:

1. I will apply pluses (+) and minuses (-) to letter grades as appropriate.

2. CS417 students, I encourage you to complete the machine assignments. I will add extra points to your Homework grade.

3. Grade weights may be adjusted. Particular consideration will be given to the Semester Project weight.

5 Exams

Exams will be administered online through Canvas.

6 Tentative Topics

Part I*

1. MACHINE ARITHMETIC AND RELATED MATTERS
   • Machine Arithmetic and Rounding
   • The Condition of a Problem and Algorithm
2. APPROXIMATION
   • Least Squares Approximation
3. INTERPOLATION
   • Polynomial Interpolation
   • Approximation and Interpolation by Spline Functions
4. NONLINEAR EQUATIONS
   • Examples, Iteration, Convergence, and Efficiency
   • Method of False Position
   • Secant Method
   • Newton’s Method

Part II*

1. NUMERICAL DIFFERENTIATION AND INTEGRATION
   • Numerical Differentiation
   • Numerical Integration

Topics of Interest* (Time Permitting)

1. MATRIX COMPUTATIONS – SYSTEMS OF LINEAR EQUATIONS
   • Gauss Elimination and LU Factorization: Basic Algorithms
   • Iterative Methods: Basic Algorithms

* The topics covered and time spent on each topic may change based on class performance and class pacing.

6.1 Objectives

This course is designed as an introduction to the basics numerical analysis. At the end of this course students will be able to:

1. Examine the impact of finite arithmetic on computation.
2. Formulate numerical approximation problems and investigate their solutions via programming.
3. Investigate the relationship between mathematical models and their matrix representations.
4. Synthesize solutions from simpler parts.
5. Design algorithms and prove their correctness using theory/analysis as building blocks.
6. Examine the spatial complexity, temporal complexity, and computational complexity of numerical solvers.
7. Implement numerical software using existing libraries.
8. Test and verify the correctness of their own codes using model problems and principles from theory.
9. Utilize vocabulary and terminology used by engineers and applied mathematicians.
10. Summarize the literature and utilize basic software packages on numerical approximation.
11. Discuss research issues in numerical computing.

6.2 Expectations

This course covers theory oriented and math oriented topics and problems. You are expected to review required mathematics, programming, and theory as directed. If whilst reviewing you would like direction or clarification contact the instructor (via email or in the discusion board).

We discuss various notations (for math and pseudocode) in this course. Keep in mind “That it is just notation.” Familiarizing oneself with unfamiliar notations is a skill we will endeaver to develop this semester.

If you have questions… Ask the instructor The cliché “If you have a question… at least one of your classmates has the same question.” is true (especially this semester).

7 Academic Accessibility

Old Dominion University is committed to ensuring equal access to all qualified students with disabilities in accordance with the Americans with Disabilities Act. The Office of Educational Accessibility (OEA) is the campus office that works with students who have disabilities to provide and/or arrange reasonable accommodations.

• If you experience a disability which will impact your ability to access any aspect of my class, please present me with an accommodation letter from OEA so that we can work together to ensure that appropriate accommodations are available to you.

• If you feel that you will experience barriers to your ability to learn and/or testing in my class but do not have an accommodation letter, please consider scheduling an appointment with OEA to determine if academic accommodations are necessary.