A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices
Michael Lass, Stephan Mohr, Hendrik Wiebeler, Thomas D. Kühne, Christian Plessl · 2018
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.