A class of rapid algorithms for independent component analysis (ICA) is presented. This method utilizes multi-step past information with respect to an existing fixed-point style for increasing the non-Gaussianity. This can be viewed as the addition of a variable-size momentum term. The use of past information comes from the idea of surrogate optimization. There is little additional cost for either software design or runtime execution when past information is included. The speed of the algorithm is evaluated on both simulated and real-world data. The real-world data includes color images and electroencephalograms (EEGs), which are an important source of data on human-computer interactions. From these experiments, it is found that the method we present here, the RapidICA, performs quickly, especially for the demixing of super-Gaussian signals.