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DTSTART;TZID=Europe/Stockholm:20230627T193000
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UID:submissions.pasc-conference.org_PASC23_sess116_pos164@linklings.com
SUMMARY:P36 - Iterative Refinement With Hierarchical Low-Rank Precondition
ers Using Mixed Precision
DESCRIPTION:Poster\n\nThomas Spendlhofer and Rio Yokota (Tokyo Institute o
f Technology)\n\nIt has been shown that the solution to a dense linear sys
tem can be accelerated by using mixed precision iterative refinement relyi
ng on approximate LU-factorization. While most recent work has focused on
obtaining such a factorization at a reduced precision, we investigate an a
lternative via low-rank approximations. Using the hierarchical matrix form
at, we are able to benefit from the reduced complexity of the LU-factoriza
tion, while being able to compensate for the accuracy lost in the approxim
ation via iterative refinement. The resulting method is able to produce re
sults accurate to a double precision solver at a lower complexity of O (n
2 ) for certain matrices. We evaluate our approach for matrices arising fr
om BEM for 2-dimensional problems. First, an experimental analysis of the
convergence behaviour is conducted, assuring that we are able to adhere to
the same error bounds as mixed precision iterative refinement. Afterwards
, we evaluate the performance in terms of the execution time, comparing it
to a general dense solver from LAPACK and preconditioned GMRES. On large
matrices, we are able to achieve a speedup of more than 16 times when comp
ared to a dense solver.
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