1. Optimization/Learning on the GPU (supplement figure slides) CIS 665 Joe Kider

2. Pictures/Slides thanks to… Jonathan Shewchuk Nico Galoppo Jeff Bolz (Most of this was a blackboard lecture, these slides supplement that, since drawing the graphs of quadratic forms can be difficult. For the most part the lecture came from the following 3 sources: –Jonathan Richard Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain –Nico Galoppo et Al., LU-GPU: Efficient Algorithms for Solving Dense Linear Systems on Graphics Hardware – Bolz et Al., Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid

3. Gauss-Jordon

4. Graph of a quadratic form f(x) The minimum point of this surface is the solution to Ax=b

5. Contours of the quadratic form

6. Gradient f’(x) of the quadric form

7. Gradient Descent

8. Problem graphs

11. Method of Orthogonal Directions

12. Conjugate Directions

13. Gram-Schmidt Conjugation

14. Conjugate Directions Conjugate directions using the Axial unit vectors, also know As Gaussian Elimination

15. Conjugate Gradients

18. Conjugate Gradients on the GPU

20. Example Applications Just a few uses: –GPU sim demo –Heart wave demo –Flesh Simulation –Water Simulation