Optimization/Learning on the GPU (supplement figure slides)

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

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

Gauss-Jordon

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

Contours of the quadratic form

Gradient f’(x) of the quadric form

Gradient Descent

Problem graphs

Method of Orthogonal Directions

Conjugate Directions

Gram-Schmidt Conjugation

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

Conjugate Gradients

Conjugate Gradients on the GPU

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

Optimization/Learning on the GPU (supplement figure slides)