1. Complex Function Simplification Program Algorithm Daniel Chromeck and Michael Harris Presentation Date: Thursday August 12, 2008 Mentor: Dr George Antoniou Assistant Mentor: Minas Kousoulis

2. Overview Background Information Demonstration Algorithms and Examples Conclusion

3. Background Information Called the Le Verrier-Faddeev algorithm Used for image filtering Original algorithm devised by Urbain Le Verrier in 1840 Improved upon by Ludvig Faddeev in 1949

4. Demonstration Demonstration can be found at the following addresses: – http://pages.csam.montclair.edu/~chromecd/inde x_files/Page745.htm http://pages.csam.montclair.edu/~chromecd/inde x_files/Page745.htm – http://pages.csam.montclair.edu/~harrismi/index _files/Page390.htm http://pages.csam.montclair.edu/~harrismi/index _files/Page390.htm

5. Original Algorithm This algorithm is computationally expensive Informal test results Cannot run a matrix larger than 5x5 without exhausting available memory

6. Original Algorithm Example Recall: The following example will use this matrix:

7. Original Algorithm Example

10. Revised Algorithm Performs the same task as the original algorithm developed by Le Verrier Performs task without using large amounts of memory at a time

11. Revised Algorithm Example The following example will use this matrix:

12. Revised Algorithm

13. Revised Algorithm Example

16. Conclusion One dimensional program is complete Future work – implement two dimensional version of the revised algorithm