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In this paper, we describe an optimized version of a Gaussian-mixture-based acoustic model likelihood evaluation algorithm for graphical processing units (GPUs). The evaluation of these likelihoods is one of the most computationally intensive parts of automatic speech recognizers, but it can be parallelized and offloaded to GPU devices. Our approach offers a significant speed-up over the recently published approaches, because it utilizes the GPU architecture in a more effective manner. All the recent implementations have been intended only for NVIDIA graphics processors, programmed either in CUDA or OpenCL GPU programming frameworks. We present results for both CUDA and OpenCL. Further, we have developed an OpenCL implementation optimized for ATI/AMD GPUs. Results suggest that even very large acoustic models can be used in real-time speech recognition engines on computers equipped with a low-end GPU or laptops. In addition, the completely asynchronous GPU management provides additional CPU resources for the decoder part of the LVCSR. The optimized implementation enables us to apply fusion techniques together with evaluating many (10 or even more) speaker-specific acoustic models. We apply this technique to a real-time parliamentary speech recognition system where the speaker changes frequently.