Algorithmic fault tolerance using the Lanczos method

We consider the problem of algorithm-based fault tolerance, and make two major contributions. First, we show how very general sequences of polynomials can be used to generate the checksums, so as to reduce the chance of numerical overows. Second, we show how the Lanczos process can be applied in the error location and correction steps, so as to save on the amount of work and to facilitate actual hardware implementation