A new error analysis based method for tolerance computation for algorithm-based checks

Algorithm based techniques are based on checking for the preservation of certain properties possessed by global data following a set of computations. This often involves the introduction of a check variable which is updated in such a manner that, in the absence of roundoff errors, it equals the value of some function which involves all the data elements participating in the algorithm. However, roundoff errors accumulate in different ways in the updates involving the check variables and the computations involving data elements; this makes it highly unlikely that the equality is preserved exactly for an implementation of the algorithm on a real computer. Thus, the check step involves verifying the preservation of the equality to within a tolerance value. We propose a method for determination of the tolerance based on error analysis techniques. We present results on three numerical algorithms which show the effectiveness of our approach for data sets of varying sizes and data ranges