In this paper we address the acceleration of the Hermite function characterization of the heartbeat by means of massively parallel Graphics Processing Units. This characterization can be used to develop tools to help the cardiologist to study and diagnose heart disease. However, obtaining this characterization, especially when a large number of functions is used to achieve a high accuracy in heartbeat representation, is very resource intensive. This paper addresses off-line and on-line heartbeat characterization, assessing the acceleration capabilities of Graphics Processing Units for these tasks. Polynomials up to the 30th order are used in the study. The results yield that the off-line processing of long electrocardiogram recordings with a GPU can be computed up to 186 faster than a standard CPU, while real-time processing can be up to 110x faster.