  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.
