Recent developments in programmable, highly parallel Graphics Processing Units (GPUs) have enabled high performance implementations of machine learning algorithms. We describe a solver for Support Vector Machine training, using Platt's Sequential Minimal Optimization algorithm and an adaptive first and second order working set selection heuristic, which achieves speedups of 9-35x over LIBSVM running on a traditional processor. We also present a GPU-based system for SVM classification which achieves speedups of 81-138x over LibSVM (5-24x over our own CPU-based SVM classifier).