Gaussian Elimination and Back Substitution Aleksandra Cerovi 03282010

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

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

Introduction-Maxeler • • Dataflow paradigm • 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 The write to the memory is postponed until the data processing is finished As less data dependences as possible Gaussian Elimination And Back Substitution 3/15

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 • Example: system of linear equations: Gaussian Elimination And Back Substitution 4/15

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

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

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

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

Details Gaussian Elimination And Back Substitution 9/15

Details Gaussian Elimination And Back Substitution 10/15

Details Gaussian Elimination And Back Substitution 11/15

Results Gaussian Elimination And Back Substitution 12/15

Conclusion Gaussian Elimination And Back Substitution 13/15

References • Milutinovic, V. , Salom, J. , Trifunovic, N. , Giorgi, R. , “Guide to Data. Flow Super. Computing”, Springer, 2015. • Milutinovic, V. , editor, “Advances in Computers: Data. Flow”, Elsevier, 2015. • Milutinovic, V. , editor, “High-Level Language Computer Architecture, “ (Chapter 9, Data. Flow 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 Max. Compiler Examples”, 2015. • -, “Gaussian elimination”, https: //en. wikipedia. org/wiki/Gaussian_elimination, 2016. Gaussian Elimination And Back Substitution 14/15