English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Current dense symmetric eigenvalue (EIG) and singular value decomposition(SVD) implementations may suffer from the lack of concurrency during thetridiagonal and bidiagonal reductions, respectively. This performancebottleneck is typical for the two-sided transformations due to the Level-2 BLASmemory-bound calls. Therefore, the current state-of-the-art EIG and SVDimplementations may achieve only a small fraction of the system's sustainedpeak performance. The QR-based Dynamically Weighted Halley (QDWH) algorithm maybe used as a pre-processing step toward the EIG and SVD solvers, whilemitigating the aforementioned bottleneck. QDWH-EIG and QDWH-SVD expose moreparallelism, while relying on compute-bound matrix operations. Both run closerto the sustained peak performance of the system, but at the expense ofperforming more FLOPS than the standard EIG and SVD algorithms. In this paper,we introduce a new QDWH-based solver for computing the partial spectrum for EIG(QDWHpartial-EIG) and SVD (QDWHpartial-SVD) problems. By optimizing therational function underlying the algorithms only in the desired part of thespectrum, QDWHpartial-EIG and QDWHpartial-SVD algorithms efficiently compute afraction (say 1-20%) of the corresponding spectrum. We develop high-performanceimplementations of QDWHpartial-EIG and QDWHpartial-SVD on distributed-memoryanymore systems and demonstrate their numerical robustness. Experimentalresults using up to 36K MPI processes show performance speedups forQDWHpartial-SVD up to 6X and 2X against PDGESVD from ScaLAPACK and KSVD,respectively. QDWHpartial-EIG outperforms PDSYEVD from ScaLAPACK up to 3.5X butremains slower compared to ELPA. QDWHpartial-EIG achieves, however, a betteroccupancy of the underlying hardware by extracting higher sustained peakperformance than ELPA, which is critical moving forward with accelerator-basedsupercomputers.

High-Performance Partial Spectrum Computation for Symmetric eigenvalue problems and the SVD