Gaussian Elimination and Back Substitution Aleksandra Cerović 0328/2010 Elektrotehnički fakultet u Beogradu Mikroprocesorski sistemi 1/12Gaussian Elimination With Back Substitution

Sadržaj 2/12 Introduction Probleam statement Existing solutions Proposed solutions Details Conclusion References Gaussian Elimination With Back Substitution

Introduction  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 With Back Substitution3/12

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 4/12Gaussian Elimination With Back Substitution

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. 5/12Gaussian Elimination With Back Substitution

C program could be written as follows: 6/12Gaussian Elimination With Back Substitution Existing solutions

Swapping of elements can be done independently... Proposed solutions 7/12Gaussian Elimination With Back Substitution

8/12 Details Gaussian Elimination With Back Substitution

9/12 Details-one iteration Gaussian Elimination With Back Substitution

Conclusion 10/12Gaussian Elimination With Back Substitution

References 11/12Gaussian Elimination With Back Substitution 1.Numerical Recipes in C –The Art of Scientifing Computing, William H.Press 2.Selected MaxCompiler Examples, Živoin Šuštran, Saša Stojanović 3.Multiscale Dataflow Programming-Tutorials 4.