Performance Evaluation of Golub-Kahan-Lanczos Algorithm with Reorthogonalization by Classical Gram-Schmidt Algorithm and OpenMP

摘要

The Golub-Kahan-Lanczos algorithm with reorthogonalization (GKLR algorithm) is an algorithm for computing a subset of singular triplets for large-scale sparse matrices. The reorthogonalization tends to become a bottleneck of elapsed time, as the iteration number of the GKLR algorithm increases. In this paper, OpenMP-based parallel implementation of the classical Gram-Schmidt algorithm with reorthogonalization (0MP-CGS2 algorithm) is introduced. The 0MP-CGS2 algorithm has the advantage of data reusability and is expected to achieve higher performance of the reorthogonalization computations on shared-memory multi-core processors with large caches than the conventional reorthogonalization algorithms. Numerical experiments on shared-memory multi-core processors show that the OMP-CGS2 algorithm accelerates the GKLR algorithm more effectively for computing a subset of singular triplets for a sparse matrix than the conventional reorthogonalization algorithms.