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Astrophysical radio signals are excellent probes of extreme physical processes that emit them. However, to reach Earth, electromagnetic radiation passes through the ionized interstellar medium, introducing a frequency-dependent time delay (dispersion) to the emitted signal. Removing dispersion enables searches for transient signals like fast radio bursts or repeating signals from isolated pulsars or those in orbit around other compact objects. The sheer volume and high resolution of data that next-generation radio telescopes will produce require high-performance computing solutions and algorithms to be used in time-domain data-processing pipelines to extract scientifically valuable results in real time. This paper presents a state-of-the-art implementation of brute force incoherent dedispersion on NVIDIA graphics-processing units and on Intel and AMD central-processing units. We show that our implementation is 4x faster (8-bit 8192 channels input) than other available solutions, and we demonstrate, using 11 existing telescopes, that our implementation is at least 20x faster than real time. This work is part of the AstroAccelerate package.