Performance Evaluation of Accelerated Complex Multiple-Precision LU Decomposition

The direct method is one of the most important algorithms for solving linear systems of equations, with LU decomposition depleting a significant portion of the computation time. This study explores strategies for accelerating complex LU decomposition, using multiple-precision floating-point arithmetic of the multiple-component type. Specifically, the potential efficiency gains are explored using a combination of single instruction and multiple data stream (SIMD) and the 3M method for complex matrix multiplication. This approach was compared with the implementation of the direct method in MPLAPACK, using benchmark tests focusing on computation time and numerical errors.