Direct linear time solvers for sparse matrices
نویسندگان
چکیده
In the last couple of years it has been realized that Gaussian elimination for sparse matrices arising from certain elliptic PDEs can be done in O(n log(1/ )) flops, where n is the number of unknowns and is a user-specified tolerance [Chandrasekaran and Gu]. The resulting solver will also be backward stable with an error of O( ). The techniques used to achieve this speedup has some commonality with ideas from domain decomposition, multi-grid, incomplete factorizations, and other areas. However, the algorithms have also shown speedups on random sparse positive-definite matrices, making it clear that some novel ideas are at play.
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