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Optimization/Learning on the GPU (supplement figure slides)

Optimization/Learning on the GPU (supplement figure slides)

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Optimization/Learning on the GPU (supplement figure slides)

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  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

  9. Method of Orthogonal Directions

  10. Conjugate Directions

  11. Gram-Schmidt Conjugation

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

  13. Conjugate Gradients

  14. Conjugate Gradients

  15. Conjugate Gradients

  16. Conjugate Gradients on the GPU

  17. Conjugate Gradients on the GPU

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