  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.
