Parallel reduction to hessenberg form with algorithm-based fault tolerance

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 Reduct...

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Veröffentlicht in:2013 SC - International Conference for High Performance Computing, Networking, Storage and Analysis (SC) S. 1 - 11
Hauptverfasser: Jia, Yulu, Bosilca, George, Luszczek, Piotr, Dongarra, Jack J.
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: New York, NY, USA ACM 17.11.2013
Schriftenreihe:ACM Conferences
Schlagworte:
Algorithm design and analysis
Algorithm-based fault tolerance
Checkpointing
Computer Science
Dense linear algebra
Eigenvalues and eigenfunctions
Engineering
Fault tolerance
Fault tolerant systems
Hessenberg reduction
Libraries
Mathematics of computing > Mathematical software
Parallel numerical libraries
Prediction algorithms
ScaLAPACK
hessenberg reduction
algorithm-based fault tolerance
ScaLAPACK
dense linear algebra
parallel numerical libraries
ISBN:9781450323789, 1450323782
ISSN:2167-4329
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:NONE
USDOE Office of Science (SC)
ISBN:9781450323789
1450323782
ISSN:2167-4329
DOI:10.1145/2503210.2503249