A Hybrid Factorization Algorithm for Sparse Matrix with Mixed Precision Arithmetic

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.
Comment: 12 pages, 4 figures, submitted to proceedings of ECCOMAS Congress 2022