A Parallel Tiled Solver for Dense Symmetric Indefinite Systems on Multicore Architectures
The authors describe an efficient and innovative parallel tiled algorithm for solving symmetric indefinite systems on multicore architectures. This solver avoids pivoting by using a multiplicative preconditioning based on symmetric randomization. This randomization prevents the communication overhead due to pivoting, is computationally inexpensive and requires very little storage. Following randomization, a tiled LDLT factorization is used that reduces synchronization by using static or dynamic scheduling. They compare Gflop/s performance of their solver with other types of factorizations on a current multicore machine and they provide tests on accuracy using LAPACK test cases.