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In order to perform big-data analytics, regression involving large matrices is often necessary. In particular, large scale regression problems are encountered when one wishes to extract semantic patterns for knowledge discovery and data mining. When a large matrix can be processed in its factorized form, advantages arise in terms of computation, implementation, and data-compression. In this work, we propose two new parallel iterative algorithms as extensions of the Gauss–Seidel algorithm (GSA) to solve regression problems involving many variables. The convergence study in terms of error-bounds of the proposed iterative algorithms is also performed, and the required computation resources, namely time- and memory-complexities, are evaluated to benchmark the efficiency of the proposed new algorithms. Finally, the numerical results from both Monte Carlo simulations and real-world datasets are presented to demonstrate the striking effectiveness of our proposed new methods.

New Efficient Approach to Solve Big Data Systems Using Parallel Gauss–Seidel Algorithms