PIOD: an Efficient Parallel Iterative Algorithm for Solving Over-determined Equations

The solution of over-determined equations plays a very important role in fields such as data fitting, signal processing, and machine learning. It is of great significance in predicting natural phenomena, optimizing engineering design, and other fields. However, there is currently no efficient method to solve over-determined equations, either being not accurate enough or consuming a lot of time. In this article, we propose a parallel iterative method for solving over-determined equations, called the PIOD algorithm. By using a sub-convergence condition to terminate the iterative calculation, we have developed a task partitioning strategy for the algorithm and implemented parallelization of the solution of over-determined equations on a distributed memory system. Our proposed algorithm achieves an average speedup of 152 ×times compared to the open-source Eigen solver. Additionally, it also achieves a parallel efficiency of over 30%.