Virtually all software requiring extensive numerical processing could benefit from the solvers developed in this project. There are numerous software packages that are already built on BLAS or higher-level libraries such as LAPACK that require BLAS. Using the technology developed in this project, such software would therefore not need to be modified to take advantage of the emerging class of hardware accelerators from companies such as NVIDIA, Intel, AMD, and others. This can have an immediate impact on numerous NASA applications such as vibration analysis for a number of multi-body spacecraft configurations such as the Crew Exploration Vehicle (CEV), the Crew Launch Vehicle (CLV), and rotorcraft and computational fluid dynamics for spacecraft flight through the atmosphere and rocket design. Other application areas of interest to NASA include weather and climate modeling, mechanical and stress modeling, heat transfer analysis, and signal/image processing. These libraries are fundamental to high-performance computing and will be required for the next generation of hardware being released. These solvers could be integrated into everything from specialized computational engines to general purpose tools such as MATLAB. MATLAB currently integrates BLAS compliant routines to solve computationally intense problems. Some versions of MATLAB even ship multiple implementations of this interface and allow the user to select between them. The solvers developed here could simply become another option for users to select, thereby offloading processing to an accelerator device such as a GPU. Specific application areas include automotive design, civil and mechanical engineering analysis, electromagnetic simulations, computational fluid dynamics, acoustics, signal/image processing, and financial modeling. There are many companies now taking advantage of GPUs to accelerate their software. Unfortunately, because of the tools available, they are mostly only compatible with NVIDIA GPUs. By using the OpenCL-based libraries we develop here, developers will be able to take advantage of all the available and emerging hardware devices such as GPUs from NVIDIA and AMD/ATI, x86 and ARM-based microprocessors, and other accelerator platforms such as the soon-to-be-released Knights Ferry from Intel.