10.1145/3218176.3218231
Lass, Michael
Michael
Lass0000-0002-5708-7632
Mohr, Stephan
Stephan
Mohr
Wiebeler, Hendrik
Hendrik
Wiebeler
Kühne, Thomas
Thomas
Kühne
Plessl, Christian
Christian
Plessl0000-0001-5728-9982
A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices
ACM
2018
2018-03-22T10:53:01Z
2019-07-23T12:13:45Z
conference
https://ris.uni-paderborn.de/record/1590
https://ris.uni-paderborn.de/record/1590.json
978-1-4503-5891-0/18/07
1710.10899
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. Following the idea of Approximate Computing, we allow imprecision in the final result in order to utilize the sparsity of the input matrix and to allow massively parallel execution. For an n x n matrix, the proposed algorithm allows to distribute the calculations over n nodes with only little communication overhead. The result matrix exhibits the same sparsity pattern as the input matrix, allowing for efficient reuse of allocated data structures.
We evaluate the algorithm with respect to the error that it introduces into calculated results, as well as its performance and scalability. We demonstrate that the error is relatively limited for well-conditioned matrices and that results are still valuable for error-resilient applications like preconditioning even for ill-conditioned matrices. We discuss the execution time and scaling of the algorithm on a theoretical level and present a distributed implementation of the algorithm using MPI and OpenMP. We demonstrate the scalability of this implementation by running it on a high-performance compute cluster comprised of 1024 CPU cores, showing a speedup of 665x compared to single-threaded execution.