This thesis delves into the field of general purpose computation on graphicsprocessing units (GPGPU). A MATLAB interface for solving numericallinear algebra on the graphics processing unit (GPU), and three algorithmsfrom numerical linear algebra are presented. The algorithms are shown tobe faster than the highly efficient ATLAS implementations used in MATLAB.In addition, the interface allows background processing on the GPU,enabling it to be used as a mathematical coprocessor. The computations areshown to be sufficiently accurate, and solving the shallow water equationsimplicitly is shown where both the CPU and the GPU are both utilized formaximumperformance. A comparison of the interface and other high-levellanguages for GPGPU is also presented.