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

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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 the Axial unit vectors, also know As Gaussian Elimination

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Conjugate Gradients

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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

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