Learn how to develop fast and energy-efficient linear solvers using GPUs. Hybrid CPU-GPU techniques achieve high performance at the cost of extra power consumption. The new advancements in GPU architectures enable full GPU solutions that are high performance, energy efficient, and CPU-independent. In addition, new technologies such as half precision arithmetic (FP16) help the design of new solvers that are significantly faster and even more energy efficient. While FP16 arithmetic has been a powerful tool for deep learning applications, our designs show that it is also very useful for boosting performance and energy efficiency of linear solvers. The new developments complement the hybrid algorithms in the MAGMA library, and provide users with a wide variety of designs that fit different requirements of performance, energy efficiency, and numerical accuracy.