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The direct method is one of the most important algorithms for solving linear systems of equations, with LU decomposition comprising a significant portion of its computation time. This study explores strategies to accelerate complex LU decomposition using multiple-precision floating-point arithmetic of the multiple-component type. Specifically, we explore the potential efficiency gains using a combination of SIMDization and the 3M method for complex matrix multiplication. Our benchmark tests compare this approach with the direct method implementation in MPLAPACK, focusing on computation time and numerical errors.
Tomonori Kouya (Sun,) studied this question.