We present performance results for dense linear algebra using the 8-series NVIDIA GPUs. Our GEMM routine runs 60% faster than the vendor implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80-90% of the peak GEMM rate. Our parallel LU running on two GPUs achieves up to ~300 Gflop/s. These results are accomplished by challenging the accepted view of the GPU architecture and programming guidelines. We argue that modern GPUs should be viewed as multithreaded multicore vector units. We exploit register blocking to optimize GEMM and heterogeneity of the system (compute both on GPU and CPU). This study includes detailed benchmarking of the GPU memory system that reveals sizes and latencies of caches and TLB. We present a couple of algorithmic optimizations aimed at increasing parallelism and regularity in the problem that provide us with slightly higher performance.