Mathematical Computation on High-dimensional Data via Array Programming and Parallel Acceleration

The exponential growth of digitalization has led to the development of new techniques, in both domains of hardware (e.g., device miniaturization and semiconductor process) and software (e.g., data structure designed for efficient data query) [1-6]. Since the data governance becomes more standardized, with the decreasing cost of data acquisition as well as the increasing maturity of associated algorithms, the validation of approaches in the experimental stage that utilize data in a production environment becomes theoretically achievable. While the majority of manipulations and calculations on data in the production environment are undergoing the stage of applying essential statistical approaches on extremely large-scale data, which catalyzes the formation of some big data related techniques such as distributed computation [7,8]. Despite the substantial advantages of distributed frames as an representative solution for parallel acceleration, the current observations indicate that they are more suitable for simple data storage, retrieval, and modification in business contexts. However, they are not well-suited for mathematical computations in exploratory purposes [9,10].