A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver for multiple right-hand sides using block GCR method with the factorization in lower precision as a preconditioner, which achieves mixed precision arithmetic, and then the Schur complement will be factorized in higher precision. In this algorithm, essential procedure is decomposition of the matrix into a union of moderate and hard parts, which is realized by LDU-factorization in lower precision with symmetric pivoting and threshold postponing technique.
翻译:提出了一个新的混合算法,用于将迭代求解器混合在一起的大型稀薄矩阵的LDU-因子化,它可以保持与典型因子化的准确性相同。最后一个Schur补充法将由使用块状GCR方法的多个右侧的迭代求解器产生,以较低精确度作为先决条件,实现混合精确算术,然后Schur补充法将以更高的精确度来计算。在这一算法中,基本程序是将矩阵分解成中硬部分的组合,通过低精度的LDU-因子化和临界延迟技术实现。