1. Gaussian Elimination and Back Substitution Aleksandra Cerović 0328/2010 1/15Gaussian Elimination And Back Substitution

2. Content 2/15 Introduction Probleam statement Existing solutions Proposed solutions Details Conclusion References Gaussian Elimination And Back Substitution

3. Introduction-Maxeler Dataflow paradigm The write to the memory is postponed until the data processing is finished Decreases cost of reading and writing temporary results Tokens on the entry points of vertices in a graph are a condition for operation completition Loop oriented, big data As less data dependences as possible Gaussian Elimination And Back Substitution3/15

4. Introduction -Gaussian Elimination Gaussian elimination reduces a matrix not all the way to the identity matrix, but only halfway, to a matrix whose components on the diagonal and above (say) remain nontrivial Gaussian Elimination And Back Substitution4/15 Example: system of linear equations:

5. Introduction -Back Substitution The procedure defined by next equation is called backsubstitution. The combination of Gaussian elimination and backsubstitution yields a solution to the set of equations. Gaussian Elimination And Back Substitution 5/15

6.  Example: Implementation of Gaussian elimination and backsubstitution in programming language c 6/15Gaussian Elimination And Back Substitution Existing solutions

7.  Swapping of elements can be done independently... Proposed solutions 7/15Gaussian Elimination And Back Substitution

8.  Swapping of elements can be done independently... Proposed solutions 8/15Gaussian Elimination And Back Substitution

9. Details Gaussian Elimination And Back Substitution 9/15

10. Gaussian Elimination And Back Substitution10/15 Details

11. Gaussian Elimination And Back Substitution 11/15 Details

12. 12/15 Results Gaussian Elimination And Back Substitution

13. Conclusion 13/15Gaussian Elimination And Back Substitution

14. References 14/15Gaussian Elimination And Back Substitution Milutinovic, V., Salom, J., Trifunovic, N., Giorgi, R., “Guide to DataFlow SuperComputing”, Springer, 2015. Milutinovic, V., editor, “Advances in Computers: DataFlow”, Elsevier, 2015. Milutinovic, V., editor, “High-Level Language Computer Architecture,“ (Chapter 9, DataFlow Machines, Gaudiot, J.-L.,), Computer Science Press, 1989. Press, W., Teukolsky, S., Vetterling, W., Flanner, B., “Numerical Recipes in C – The Art of Scientifing Computing”, Cambridge University Press, 1992. Sustran, Z., Stojanovic, S., “Selected MaxCompiler Examples”, 2015. -, “Gaussian elimination”, https://en.wikipedia.org/wiki/Gaussian_elimination, 2016.