Parallel reduction to hessenberg form with algorithm-based fault tolerance

Conference · Tue Jan 01 04:00:00 EST 2013 · 2013 INTERNATIONAL CONFERENCE FOR HIGH PERFORMANCE COMPUTING, NETWORKING, STORAGE AND ANALYSIS (SC)

DOI:https://doi.org/10.1145/2503210.2503249· OSTI ID:1567343

Jia, Yulu; Bosilca, George; Luszczek, Piotr; Dongarra, Jack J.

This paper studies the resilience of a two-sided factorization and presents a generic algorithm-based approach capable of making two-sided factorizations resilient. We establish the theoretical proof of the correctness and the numerical stability of the approach in the context of a Hessenberg Reduction (HR) and present the scalability and performance results of a practical implementation. Our method is a hybrid algorithm combining an Algorithm Based Fault Tolerance (ABFT) technique with diskless checkpointing to fully protect the data. We protect the trailing and the initial part of the matrix with checksums, and protect finished panels in the panel scope with diskless checkpoints. Compared with the original HR (the ScaLAPACK PDGEHRD routine) our fault-tolerant algorithm introduces very little overhead, and maintains the same level of scalability. We prove that the overhead shows a decreasing trend as the size of the matrix or the size of the process grid increases.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
• Sponsoring Organization: USDOE Office of Science (SC)
• OSTI ID: 1567343
• Conference Information: Journal Name: 2013 INTERNATIONAL CONFERENCE FOR HIGH PERFORMANCE COMPUTING, NETWORKING, STORAGE AND ANALYSIS (SC)
• Country of Publication: United States
• Language: English

Related Subjects

Computer Science
Engineering