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DTSTAMP:20230831T095746Z
LOCATION:Davos
DTSTART;TZID=Europe/Stockholm:20230627T100700
DTEND;TZID=Europe/Stockholm:20230627T100800
UID:submissions.pasc-conference.org_PASC23_sess110_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.\n\nSession Chair: Jibonananda Sanyal (National Ren
 ewable Energy Laboratory)
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