Abstract
We introduced a unified checksum method for multiple transient error detection in three different matrix triangularizations: the LU decomposition, Gaussian elimination with pairwise pivoting, and the QR decomposition. We first develop the theoretical back-ground for multiple error detection in matrix triangularizations, and summarize the results by providing that we can detect all the transient errors that occur in a maximum of t different columns by introducing t checksum vectors. A floating-point error analysis, to determine the effects of the rounding errors in using the checksum method for multiple error detection and correction, is also presented.
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