OpenCL Joseph Kider University of Pennsylvania CIS 565 - Fall 2011.
Optimization/Learning on the GPU (supplement figure slides) CIS 665 Joe Kider.
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Transcript of Optimization/Learning on the GPU (supplement figure slides) CIS 665 Joe Kider.
![Page 1: Optimization/Learning on the GPU (supplement figure slides) CIS 665 Joe Kider.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649d6a5503460f94a48125/html5/thumbnails/1.jpg)
Optimization/Learning on the GPU (supplement figure slides)
CIS 665
Joe Kider
![Page 2: Optimization/Learning on the GPU (supplement figure slides) CIS 665 Joe Kider.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649d6a5503460f94a48125/html5/thumbnails/2.jpg)
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
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Gauss-Jordon
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Graph of a quadratic form f(x)
The minimum point of this surface is the solution to Ax=b
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Contours of the quadratic form
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Gradient f’(x) of the quadric form
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Gradient Descent
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Problem graphs
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Method of Orthogonal Directions
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Conjugate Directions
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Gram-Schmidt Conjugation
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Conjugate Directions
Conjugate directions using theAxial unit vectors, also knowAs Gaussian Elimination
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Conjugate Gradients
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Conjugate Gradients
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Conjugate Gradients
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Conjugate Gradients on the GPU
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Conjugate Gradients on the GPU
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Example Applications
• Just a few uses:
– GPU sim demo– Heart wave demo– Flesh Simulation– Water Simulation