Résumé : In this chapter, we present a hybridization methodology for the development of linear algebra software for GPUs. The methodology is successfully used in MAGMA – a new generation of linear algebra libraries, similar in functionality to LAPACK, but extended for hybrid, GPU-based systems. Algorithms of interest are split into computational tasks. The tasks' execution is scheduled over the computational components of a hybrid system of multicore CPUs with GPU accelerators using StarPU – a runtime system for accelerator-based multicore architectures. StarPU enables to express parallelism through sequential-like code and schedules the different tasks over the hybrid processing units. The productivity becomes then fast and cheap as the development is high level, using existing software infrastructure. Moreover, the resulting hybrid algorithms are better performance-wise than corresponding homogeneous algorithms designed exclusively for either GPUs or homogeneous multicore CPUs.