- Option A (Experimental
evaluation):

- Pick an application domain that interests you.
- Identify a problem in that application domain that can be formulated as a large linear system.
- Implement and experiment with several techniques to tackle this linear system.
- Option B (Algorithm design):

- Identify a class of linear systems for which existing techniques do not scale well.
- Develop a new technique (data structure and/or algorithm) to better tackle this class of linear systems.
- Implement your approach and compare it empirically to other existing approaches.
- Option C (Mathematical Analysis):

- Identify a technique for which the mathematical properties (e.g., scalability, stability, convergence) are not well understood.
- Analyze mathematically the properties of this technique.
- Verify empirically the conclusions resulting from your mathematical analysis.

- Submit by October 9

- At most one page
- Which option did you pick?
- Option A:

- What is the application domain?
- What is the problem you plan to formulate as a linear system?
- Which techniques do you plan to experiment with?
- Option B:
- What class of linear systems will you design a new technique for?
- What properties would you like this new technique to have?
- Option C:
- What technique do you plan to analyze?
- What properties would you like to analyze/prove about this
technique?

- Cite 4-8 papers related to the topic of your project that you plan to survey.

- At most 8 pages
**Hand in at the final exam**

- Option A:
- Introduction
- What is the application domain?

- What is the problem? How do you formulate it as a linear system?
- Techniques to tackle the problem

- Brief survey of previous work concerning this problem (i.e., the 4-8 papers that you read)
- Brief description of the techniques chosen and why

- Empirical evaluation

- Compare empirically the techniques for scalability, stability, convergence, ease of use, etc.
- Conclusion:
- What is the best technique?

- Is any technique good enough to solve the linear system?
- What future research do you recommend?
- Option B:
- Introduction
- What class of linear systems are you considering?
- Why can't any of the existing techniques effectively tackle
this class?

- Techniques to tackle the problem

- Brief survey of previous work concerning this problem (i.e., the 4-8 papers that you read)
- Describe the technique that you developed
- Brief description of the existing techniques that you will
compare to

- Empirical evaluation

- Evaluate empirically the technique that you developed
- How does it compare to some of the existing techniques?
- Conclusion:
- Can your technique effectively tackle the class of linear systems considered?
- What future research do you recommend?
- Option C:
- Introduction
- What technique are you analyzing?
- What properties did you analyze/prove about this technique?

- Analysis

- Brief survey of previous work concerning this problem (i.e., the 4-8 papers that you read)
- Describe the analysis performed

- Empirical evaluation

- Verify empirically the analysis performed
- Conclusion:
- What have you discovered about the technique analyzed?
- What future research do you recommend?