论文标题
稀疏精度算术的稀疏基质的混合分解算法
A Hybrid Factorization Algorithm for Sparse Matrix with Mixed Precision Arithmetic
论文作者
论文摘要
提出了一种新的用于LDU因子化的混合算法，用于结合迭代求解器的大型稀疏基质，可以保持与经典分解相同的准确性。迭代求解器将使用块GCR方法以较低的精度为预处理，将产生最后的SCHUR补体，用于多个右侧，以较低的精度为先进器，该方法可实现混合精度算术，然后将Schur补体以较高的精度分解。在该算法中，基本过程是矩阵分解为中等和硬零件的结合，这是通过LDU因素化在较低精度的情况下实现的，并具有对称的枢纽和阈值推迟技术。
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.
