Multiple Error Algorithm-Based Fault Tolerance For Matrix Triangularizations

Haesun Park

doi:10.1117/12.948509

23 February 1988 Multiple Error Algorithm-Based Fault Tolerance For Matrix Triangularizations

Haesun Park

Proceedings Volume 0975, Advanced Algorithms and Architectures for Signal Processing III; (1988) https://doi.org/10.1117/12.948509
Event: 32nd Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1988, San Diego, CA, United States

Abstract

The checksum methods have been known as the most efficient fault-tolerant matrix triangularization schemes on systolic arrays in the presence of a single transient error. But it is not realistic to expect that at most one transient error occurs during any computation. In this paper, we extend the existing checksum schemes and introduce a block checksum scheme for multiple transient errors applicable to the fault tolerant matrix LU decomposition, Gaussian elimination with pairwise pivoting, and the QR decomposition. The block checksum scheme can detect, locate, and correct one transient error in each submatrix of a given matrix. Then we introduce examples that show that even one transient error can make the corrected results by factorization updates useless due to rounding errors. We also show that by introducing d weighted checksum vectors, we can detect all the transient errors that occur in a maximum of d different columns in matrix triangularizations.

Citation Download Citation

Haesun Park "Multiple Error Algorithm-Based Fault Tolerance For Matrix Triangularizations", Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); https://doi.org/10.1117/12.948509

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