The design and use of a sparse direct solver for skew symmetric matrices
Journal of Computational and Applied Mathematics
A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Reducing the I/O Volume in Sparse Out-of-core Multifrontal Methods
SIAM Journal on Scientific Computing
Partial factorization of a dense symmetric indefinite matrix
ACM Transactions on Mathematical Software (TOMS)
Direct sparse factorization of blocked saddle point matrices
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Pivoting strategies for tough sparse indefinite systems
ACM Transactions on Mathematical Software (TOMS)
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We consider the direct solution of sparse symmetric indefinite matrices. We develop new pivoting strategies that combine numerical pivoting and perturbation techniques. Then an iterative refinement process uses our approximate factorization to compute a solution. We show that our pivoting strategies are numerically robust, that few steps of iterative refinement are required, and that the factorization is significantly faster than with previous methods. Furthermore, we propose original approaches that are designed for parallel distributed factorization. A key point of our parallel implementation is the cheap and reliable estimation of the growth factor. This estimation is based on an approximation of the off-diagonal entries and does not require any supplementary messages.