P36 - Iterative Refinement With Hierarchical Low-Rank Preconditioners Using Mixed Precision
DescriptionIt has been shown that the solution to a dense linear system can be accelerated by using mixed precision iterative refinement relying on approximate LU-factorization. While most recent work has focused on obtaining such a factorization at a reduced precision, we investigate an alternative via low-rank approximations. Using the hierarchical matrix format, we are able to benefit from the reduced complexity of the LU-factorization, while being able to compensate for the accuracy lost in the approximation via iterative refinement. The resulting method is able to produce results accurate to a double precision solver at a lower complexity of O (n 2 ) for certain matrices. We evaluate our approach for matrices arising from 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 compared to a dense solver.
TimeTuesday, June 2710:07 - 10:08 CEST