In manufacturing, metrological inspection is a time-consuming process. The higher the required precision in inspection, the longer the inspection time. This is due to both slow devices that collect measurement data and slow computational methods that process the data. The goal of this work is to propose methods to speed up some of these processes. Conventional measurement devices like Coordinate Measuring Machines (CMMs) have high precision but low measurement speed while new digitizer technologies have high speed but low precision. Using these devices in synergy gives a significant improvement in the measurement speed without loss of precision. The method of synergistic integration of an advanced digitizer with a CMM is discussed. Computational aspects of the inspection process are addressed next. Once a part is measured, measurement data is compared against its model to check for tolerances. This comparison is a time-consuming process on conventional CPUs. We developed and benchmarked some GPU accelerations. Finally, naive data fitting methods can produce misleading results in cases with non-uniform data. Weighted total least-squares methods can compensate for non-uniformity. We show how they can be accelerated with GPUs, using plane fitting as an example. / Thesis / Doctor of Philosophy (PhD)