Investigating the Use of Pipelined LU Decomposition to Solve Systems of Linear Equations

Large linear systems are used in many applications, and millions of equations can be utilized (e.g., in aircraft manufacturing). These equations need to be simplified, which allows faster processing and easier implementation. The LU decomposition method and its pipelined version are implemented to illustrate their efficiency. A comprehensive comparison between the sequential LU decomposition, multithreading LU decomposition, and TPL methods is conducted under different coefficient matrix block sizes to represent these systems. The results show that the multithreading and TPL approaches reduce the processing time required to compute the coefficient matrix compared to sequential processing. This finding will help improve the performance of some techniques in the literature by paralyzing the LU decomposition part of the system.