Least squares prediction is a technique used to foresee pixel values during image coding by finding the minimum square error of neighbouring pixels. It has shown considerable quality gains especially for complex images with high variations in pixel intensities. The drawback of this technique consists of high computational complexity, consuming the most significant part of processing time and resources available, which makes it difficult to implement in fast, lossy image coders. One challenge is therefore to reduce the computational time of this predictor, namely through the use of new parallel programming techniques, making it more attractive for state-of-the-art coder-decoders. Also, new algorithmic propositions are made, trying to reduce the time spent in exchange for rate-distortion performance. These propositions are senseful since this predictor is used not only in lossless image coding, but also in lossy as well. Another aim of this article is to analyze energy efficiency among different types of platforms for this signal processing algorithm. Comparisons are provided on parallel computing processors ranging from very powerful Graphics Computing Units (GPUs) to mobile General-Purpose GPUs.