Abstract
Recently, we have introduced a new preconditioner for the one-sided block-Jacobi SVD algorithm. In the serial case it outperformed the simple driver routine DGESVD from LAPACK. In this contribution, we provide the numerical analysis of applying the preconditioner in finite arithmetic and compare the performance of our parallel preconditioned algorithm with the procedure PDGESVD, the ScaLAPACK counterpart of DGESVD. Our Jacobi based routine remains faster also in the parallel case, especially for well-conditioned matrices.
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References
Anderson, A., et al.: LAPACK Users’ Guide, 3rd edn. SIAM, Philadelphia (1999)
Bečka, M., Okša, G., Vidličková, E.: New preconditioning for the one-sided block-Jacobi SVD algorithm. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds.) PPAM 2017. LNCS, vol. 10777, pp. 590–599. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78024-5_51
Bečka, M., Okša, G., Vajteršic, M.: Dynamic ordering for a parallel block Jacobi SVD algorithm. Parallel Comput. 28, 243–262 (2002). https://doi.org/10.1016/S0167-8191(01)00138-7
Bečka, M., Okša, G., Vajteršic, M.: New dynamic orderings for the parallel one-sided block-Jacobi SVD algorithm. Parallel Proc. Lett. 25, 1–19 (2015). https://doi.org/10.1142/S0129626415500036
Bečka, M., Okša, G.: Parallel one-sided Jacobi SVD algorithm with variable blocking factor. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2013. LNCS, vol. 8384, pp. 57–66. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55224-3_6
Dongarra, J., et al.: The singular value decomposition: anatomy of optimizing an algorithm for extreme scale. SIAM Rev. 60, 808–865 (2018). https://doi.org/10.1137/17M1117732
Golub, G.H., van Loan, C.F.: Matrix Computations, 4th edn. The John Hopkins University Press, Baltimore (2013)
Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM, Philadelphia (2002)
Jia, Z.: Using cross-product matrices to compute the SVD. Numer. Algorithms 42, 31–61 (2006). https://doi.org/10.1007/s11075-006-9022-x
Kudo, S., Yamamoto, Y., Bečka, M., Vajteršic, M.: Performance analysis and optimization of the parallel one-sided block-Jacobi algorithm with dynamic ordering and variable blocking. Concurr. Comput. Pract. Exp. 29, 1–24 (2017). https://doi.org/10.1002/cpe.4059
Nakatsukasa, Y., Higham, N.J.: Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. SIAM J. Sci. Comput. 35, 1325–1349 (2013). https://doi.org/10.1137/120876605
Okša, G., Yamamoto, Y., Vajteršic, M.: Asymptotic quadratic convergence of the block-Jacobi EVD algorithm for Hermitian matrices. Numer. Math. 136, 1071–1095 (2017). https://doi.org/10.1007/s00211-016-0863-5
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Authors were supported by the VEGA grant no. 2/0004/17.
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Bečka, M., Okša, G. (2020). Preconditioned Jacobi SVD Algorithm Outperforms PDGESVD. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12043. Springer, Cham. https://doi.org/10.1007/978-3-030-43229-4_47
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