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.

翻译：直接法是求解线性方程组最重要的算法之一，其中LU分解占据了其大部分计算时间。本研究探索了使用多分量类型的多精度浮点算术加速复数LU分解的策略。具体而言，我们结合SIMD化与用于复数矩阵乘法的3M方法，探究了潜在的效率提升。基准测试将本方法与MPLAPACK中直接法的实现进行了对比，重点关注计算时间和数值误差。