Accurate cardiac bidomain conductivity values are essential for realistic simulation of various cardiac electrophysiological phenomena. A method was previously developed that can determine the conductivities from measurements of potential on a multi-electrode array placed on the surface of the heart. These conductivities, as well as a value for fibre rotation, are determined using a mathematical model and a two-pass process that is based on Tikhonov regularisation. Using simulated potentials, to which noise is added, the inversion method was recently shown to retrieve the intracellular conductivities accurately with up to 15% noise and the extracellular conductivities extremely accurately even with 20% noise. Recent work investigated the sensitivity of the method to the choice of the regularisation parameters. Such a study only became possible due to modifications that were made to the C++ code so that it could run on graphical processing units (GPUs) on the CUDA platform. As the method required the solution of a large number of matrix equations, the highly parallel nature of GPUs was exploited to accelerate execution of the code. Reorganisation of the code and more efficient memory management techniques allowed the data to completely fit in the GPU memory. Comparison between the execution time on the GPU versus the original CPU code shows a speedup of up to 60 times. In the future, the speedup could be further increased with greater use of shared memory, which has a much lower latency (access time) than global memory.