Robust Fault Tolerance for Computations in Linear Algebra and Signal Processing

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The objective of this project is to develop and test fault tolerant algorithms for numerical computation in various domains, including sparse matrices, recursive filtering and signal processing. The methods used are a combination of checks made during the computation based on preconditioned checksums and thresholds, and a-posteriori checks made on the final computed results based on backward error assertions (BEAs). In spite of the presence of rounding errors, BEAs allow very tight, cheap, validation of the final results independent of the specifics of the implementation or sources of error, and checksums and thresholds supplement the BEAs by providing checks during the computation. These methods will be extended beyond prototype examples to more realistic large computations, demonstrating their scalability and applicability to large domains.***