research-article

Fault-Tolerant Matrix Triangularizations on Systolic Arrays

Authors:

H. ParkAuthors Info & Claims

IEEE Transactions on Computers, Volume 37, Issue 11

Pages 1434 - 1438

https://doi.org/10.1109/12.8712

Published: 01 November 1988 Publication History

Abstract

Examines the checksum methods of Abraham et al. for LU decomposition on multiprocessor arrays. Their methods are efficient for detecting a transient error, but expensive for correcting it due to the need for a computation rollback. The authors show how to avoid the rollback by using matrix updating techniques, and they introduce new checksum methods for Gaussian elimination with pairwise pivoting and for QR decomposition on systolic arrays.

References

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{1} J. A. Abraham, "Fault tolerant techniques for highly parallel signal processing architectures," in Highly Parallel Signal Processing Architectures, Proc. SPIE, K. Bromley, Ed., vol. 614, 1986, pp. 49-65.

[2]

{2} H. M. Ahmed, J.-M. Delosme, and M. Morf, "Highly concurrent computing structures for matrix arithmetic and signal processing," Computer, vol. 15, pp. 65-82, Jan. 1982.

Digital Library

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{3} A. Bojanczyk, R. P. Brent, and H. T. Kung, "Numerically stable solution of dense systems of linear equations using mesh-connected processors," SIAM J. Sci. Statist. Comput., vol. 5, pp. 95-104, 1984.

Digital Library

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{4} W. M. Gentleman and H. T. Kung, "Matrix triangularization by systolic arrays," in Real Time Signal Processing IV, Proc. SPIE, T. F. Tao, Ed., vol. 298, 1981, pp. 19-26.

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{5} P. E. Gill, G. H. Golub, W. Murray, and M. A. Saunders, "Methods for modifying matrix factorizations," Math. Comput., vol. 28, pp. 505-535, 1974.

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{6} K-H. Huang and J. A. Abraham, "Algorithm-based fault tolerance for matrix operations," IEEE Trans. Comput., vol. C-33, pp. 518-528, 1984.

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{7} J-Y. Jou and J. A. Abraham, "Fault-tolerant matrix arithmetic and signal processing on highly concurrent computing structures," Proc. IEEE, vol. 74, pp. 732-741, 1986.

[8]

{8} H. T. Kung and M. S. Lam, "Fault-tolerant VLSI systolic arrays and two-level pipelining," in Real Time Signal Processing VI, Proc. SPIE, K. Bromley, Ed., vol. 431, 1983, pp. 143-158.

[9]

{9} H. T. Kung and C. E. Leiserson, "Algorithms for VLSI processor arrays," in Introduction to VLSI Systems, C. Mead and L. Conway, Eds. Reading, MA: Addison-Wesley, 1980, pp. 271-292.

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{10} F. T. Luk, "Algorithm-based fault tolerance for parallel matrix equation solvers," in Real Time Signal Processing VIII, Proc. SPIE, W. J. Miceli and K. Bromley, Eds., vol. 564, 1985, pp. 49-53.

[11]

{11} F. T. Luk, "A rotation method for computing the QR-decomposition," SIAM J. Sci. Statist. Comput., vol. 7, pp. 452-459, 1986.

Digital Library

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{12} F. T. Luk and H. Park, "Analysis of algorithm-based fault tolerance techniques," in J. Parallel Distribut. Comput., vol. 5, pp. 172-184, 1988.

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{13} J. M. Ortega, Numerical Analysis, A Second Course. New York: Academic, 1972.

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{14} D. C. Sorensen, "Analysis of pairwise pivoting in Gaussian elimination," IEEE Trans. Comput., vol. C-34, pp. 274-278, 1985.

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{15} J. M. Speiser and H. J. Whitehouse, "A review of signal processing with systolic arrays," in Real Time Signal Processing VI, Proc. SPIE, K. Bromley, Ed., vol. 431, 1983, pp. 2-6.

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{16} J. H. Wilkinson, The Algebraic Eigenvalue Problem. London, England: Oxford University Press, 1965.

Cited By

Jia JLiu YZhang GGao YQian D(2022)Software approaches for resilience of high performance computing systems: a surveyFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-022-2096-317:4Online publication date: 12-Dec-2022
https://dl.acm.org/doi/10.1007/s11704-022-2096-3
Wu PDeBardeleben NGuan QBlanchard SChen JTao DLiang XOuyang KChen Z(2017)Silent Data Corruption Resilient Two-sided Matrix FactorizationsACM SIGPLAN Notices10.1145/3155284.301875052:8(415-427)Online publication date: 26-Jan-2017
https://dl.acm.org/doi/10.1145/3155284.3018750
Wu PDeBardeleben NGuan QBlanchard SChen JTao DLiang XOuyang KChen ZSarkar VRauchwerger L(2017)Silent Data Corruption Resilient Two-sided Matrix FactorizationsProceedings of the 22nd ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming10.1145/3018743.3018750(415-427)Online publication date: 26-Jan-2017
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Fault-Tolerant Matrix Triangularizations on Systolic Arrays

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cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 37, Issue 11

November 1988

174 pages

ISSN:0018-9340

Editor:
Ming T. Liu

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Copyright © Copyright © 1988 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

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Published: 01 November 1988

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Cited By

Jia JLiu YZhang GGao YQian D(2022)Software approaches for resilience of high performance computing systems: a surveyFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-022-2096-317:4Online publication date: 12-Dec-2022
https://dl.acm.org/doi/10.1007/s11704-022-2096-3
Wu PDeBardeleben NGuan QBlanchard SChen JTao DLiang XOuyang KChen Z(2017)Silent Data Corruption Resilient Two-sided Matrix FactorizationsACM SIGPLAN Notices10.1145/3155284.301875052:8(415-427)Online publication date: 26-Jan-2017
https://dl.acm.org/doi/10.1145/3155284.3018750
Wu PDeBardeleben NGuan QBlanchard SChen JTao DLiang XOuyang KChen ZSarkar VRauchwerger L(2017)Silent Data Corruption Resilient Two-sided Matrix FactorizationsProceedings of the 22nd ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming10.1145/3018743.3018750(415-427)Online publication date: 26-Jan-2017
https://dl.acm.org/doi/10.1145/3018743.3018750
Austin BRoman ELi XDeBardeleben NDeBardeleben NCappello FClay R(2015)Resilient Matrix Multiplication of Hierarchical Semi-Separable MatricesProceedings of the 5th Workshop on Fault Tolerance for HPC at eXtreme Scale10.1145/2751504.2751507(19-26)Online publication date: 15-Jun-2015
https://dl.acm.org/doi/10.1145/2751504.2751507
Jia YBosilca GLuszczek PDongarra JGropp WMatsuoka S(2013)Parallel reduction to hessenberg form with algorithm-based fault toleranceProceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis10.1145/2503210.2503249(1-11)Online publication date: 17-Nov-2013
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Du PLuszczek PTomov SDongarra JAlexandrov VGeist ADongarra J(2011)Soft error resilient QR factorization for hybrid system with GPGPUProceedings of the second workshop on Scalable algorithms for large-scale systems10.1145/2133173.2133179(11-14)Online publication date: 14-Nov-2011
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Youn HOh CChoo HChung JLee D(2001)An Efficient Algorithm-Based Fault Tolerance Design Using the Weighted Data-Check RelationshipIEEE Transactions on Computers10.1109/12.91928150:4(371-383)Online publication date: 1-Apr-2001
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Connolly MFitzpatrick P(1998)Fault Tolerant Faddeeva AlgorithmJournal of Parallel and Distributed Computing10.1006/jpdc.1998.147453:1(78-89)Online publication date: 25-Aug-1998
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Fitzpatrick P(1997)Extending Backward Error Assertions to Tolerance of Large Errors in Floating Point ComputationsIEEE Transactions on Computers10.1109/12.58807246:4(505-510)Online publication date: 1-Apr-1997
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Tao DHartmann CHan Y(1996)New Encoding/Decoding Methods for Designing Fault-Tolerant Matrix OperationsIEEE Transactions on Parallel and Distributed Systems10.1109/71.5369377:9(931-938)Online publication date: 1-Sep-1996
https://dl.acm.org/doi/10.1109/71.536937
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