Enhancing the Real-Time Solutions of Parametric Linear Systems on a GPU through Hybrid Coarse-Grained Transprecision Computing

Processing of parametric linear systems of the form G(P) := X<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⊤</sup>PX is computationally intensive as they use double precision, and matrix X can be large. Many applications can tolerate numerical errors and GPUs support a range of low-precision formats, so a hybrid coarse-grained transprecision computing approach is proposed to improve the performance under a predefined error threshold. In the offline phase, suitable low-precision formats for X and P matrices are identified. In the online phase, incoming Ps are analyzed dynamically and an appropriate low-precision format is selected for computing G(P). A 21.6M × 500 X matrix is processed 14x faster compared to its double precision version, enabling real-time evaluation of one P matrix every 2 seconds on an NVIDIA A100 GPU with an average relative error of less than 0.3%.